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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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X-WR-CALNAME:Discrete Mathematics Group
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20200101T000000
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END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210512T170000
DTEND;TZID=Asia/Seoul:20210512T180000
DTSTAMP:20260418T034111
CREATED:20210319T045925Z
LAST-MODIFIED:20240705T190026Z
UID:3816-1620838800-1620842400@dimag.ibs.re.kr
SUMMARY:Johannes Carmesin\, A Whitney type theorem for surfaces: characterising graphs with locally planar embeddings
DESCRIPTION:Given a graph\, how do we construct a surface so that the graph embeds in that surface in an optimal way? Thomassen showed that for minimum genus as optimality criterion\, this problem would be NP-hard. Instead of minimum genus\, here we use local planarity — and provide a polynomial algorithm. \nOur embedding method is based on Whitney’s trick to use matroids to construct embeddings in the plane. Consequently we obtain a characterisation of the graphs admitting locally planar embeddings in surfaces in terms of a certain matroid being co-graphic.
URL:https://dimag.ibs.re.kr/event/2021-05-12/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210511T163000
DTEND;TZID=Asia/Seoul:20210511T173000
DTSTAMP:20260418T034111
CREATED:20210420T015716Z
LAST-MODIFIED:20240705T185043Z
UID:3969-1620750600-1620754200@dimag.ibs.re.kr
SUMMARY:Mark Siggers\, The list switch homomorphism problem for signed graphs
DESCRIPTION:A signed graph is a graph in which each edge has a positive or negative sign. Calling two graphs switch equivalent if one can get from one to the other by the iteration of the local action of switching all signs on edges incident to a given vertex\, we say that there is a switch homomorphism from a signed graph $G$ to a signed graph $H$ if there is a sign preserving homomorphism from $G’$ to $H$ for some graph $G’$ that is switch equivalent to $G$.  By reductions to CSP this problem\, and its list version\, are known to be either polynomial time solvable or NP-complete\, depending on $H$.  Recently those signed graphs $H$ for which the switch homomorphism problem is in $P$ were characterised.  Such a characterisation is yet unknown for the list version of the problem. \nWe talk about recent work towards such a characterisation and about how these problems fit in with bigger questions that still remain around the recent CSP dichotomy theorem.
URL:https://dimag.ibs.re.kr/event/2021-05-11/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210506T161500
DTEND;TZID=Asia/Seoul:20210506T171500
DTSTAMP:20260418T034111
CREATED:20210427T013100Z
LAST-MODIFIED:20240705T185031Z
UID:4010-1620317700-1620321300@dimag.ibs.re.kr
SUMMARY:Hong Liu\, Sublinear expander and embeddings sparse graphs
DESCRIPTION:A notion of sublinear expander has played a central role in the resolutions of a couple of long-standing conjectures in embedding problems in graph theory\, including e.g. the odd cycle problem of Erdős and Hajnal that the harmonic sum of odd cycle length in a graph diverges with its chromatic number. I will survey some of these developments.
URL:https://dimag.ibs.re.kr/event/2021-05-06-2/
LOCATION:Zoom
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210506T100000
DTEND;TZID=Asia/Seoul:20210506T110000
DTSTAMP:20260418T034111
CREATED:20210319T045807Z
LAST-MODIFIED:20240705T190027Z
UID:3813-1620295200-1620298800@dimag.ibs.re.kr
SUMMARY:Raul Lopes\, Adapting the Directed Grid Theorem into an FPT Algorithm
DESCRIPTION:The Grid Theorem of Robertson and Seymour [JCTB\, 1986] is one of the most important tools in the field of structural graph theory\, finding numerous applications in the design of algorithms for undirected graphs. An analogous version of the Grid Theorem in digraphs was conjectured by Johnson et al. [JCTB\, 2001] \, and proved by Kawarabayashi and Kreutzer [STOC\, 2015]. They showed that there is a function f(k) such that every digraph of directed tree-width at least f(k) contains a cylindrical grid of order k as a butterfly minor and stated that their proof can be turned into an XP algorithm\, with parameter k\, that either constructs a decomposition of the appropriate width\, or finds the claimed large cylindrical grid as a butterfly minor. \nIn this talk\, we present the ideas used in our adaptation of the Directed Grid Theorem into an FPT algorithm. We provide two FPT algorithms with parameter k. The first one either produces an arboreal decomposition of width 3k-2 or finds a haven of order k in a digraph D. The second one uses a bramble B that naturally occurs in digraphs of large directed tree-width to find a well-linked set of order k that is contained in the set of vertices of a path hitting all elements of B. As tools to prove these results\, we show how to solve a generalized version of the problem of finding balanced separators for a given set of vertices T in FPT time with parameter |T|. \nJoint work with Victor Campos\, Ana Karolinna Maia\, and Ignasi Sau.
URL:https://dimag.ibs.re.kr/event/2021-05-06/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210430T090000
DTEND;TZID=Asia/Seoul:20210430T122000
DTSTAMP:20260418T034111
CREATED:20210315T005534Z
LAST-MODIFIED:20240707T081537Z
UID:3794-1619773200-1619785200@dimag.ibs.re.kr
SUMMARY:Extremal and Probabilistic Combinatorics (2021 KMS Spring Meeting)
DESCRIPTION:A special session “Extremal and Probabilistic Combinatorics” at the 2021 KMS Spring Meeting is organized by Tuan Tran. \nURL: https://www.kms.or.kr/meetings/spring2021/ \nSpeakers and Schedule\nAll talks are on April 30. \n\n[9:00 am] Joonkyung Lee (이준경)\, University College London\n\nMajority dynamics on sparse random graphs\n\n\n[9:30 am] Dong Yeap Kang (강동엽)\, Unversity of Birmingham\n\nThe Erdős-Faber-Lovász conjecture and related results\n\n\n[10:00 am] Jinyoung Park (박진영)\, IAS\n\nThe threshold for the square of a Hamilton cycle\n\n\n[10:50 am] Debsoumya Chakraborti\, IBS Discrete Mathematics Group\n\nGeneralized graph saturation\n\n\n[11:20 am] Jaehoon Kim (김재훈)\, KAIST\n\nResolution of the Oberwolfach problem\n\n\n[11:50 am] Hong Liu\, University of Warwick\n\nSublinear expanders and its applications\n\n\n\n\n\n\nAbstracts\nDebsoumya Chakraborti\, Generalized graph saturation\nGraph saturation is one of the oldest areas of investigation in extremal combinatorics. A graph G is called F-saturated if G does not contain a subgraph isomorphic to F\, but the addition of any edge creates a copy of F. We resolve one of the most fundamental questions of minimizing the number of cliques of size r in a $K_s$-saturated graph for all sufficiently large numbers of vertices\, confirming a conjecture of Kritschgau\, Methuku\, Tait and Timmons. We further prove a corresponding stability result. This talk will be based on joint work with Po-Shen Loh. \nJaehoon Kim (김재훈)\, Resolution of the Oberwolfach problem\nThe Oberwolfach problem\, posed by Ringel in 1967\, asks for a decomposition of $K_{2n+1}$ into edge-disjoint copies of a given 2-factor. We show that this can be achieved for all large n. We actually prove a significantly more general result\, which allows for decompositions into more general types of factors. \nDong Yeap Kang (강동엽)\, The Erdős-Faber-Lovász conjecture and related results\nA hypergraph is linear if every pair of two distinct edges shares at most one vertex. A longstanding conjecture by Erdős\, Faber\, and Lovász in 1972\, states that the chromatic index of any linear hypergraph on n vertices is at most n. \nIn this talk\, I will present the ideas to prove the conjecture for all large n. This is joint work with Tom Kelly\, Daniela Kühn\, Abhishek Methuku\, and Deryk Osthus. \n  \nJoonkyung Lee (이준경)\, Majority dynamics on sparse random graphs\nMajority dynamics on a graph G is a deterministic process such that every vertex updates its {-1\,1}-assignment according to the majority assignment on its neighbor simultaneously at each step. Benjamini\, Chan\, O’Donnell\, Tamuz and Tan conjectured that\, in the Erdős-Rényi random graph G(n\,p)\, the random initial {-1\,1}-assignment converges to the unanimity with high probability whenever p>> 1/n. \nThis conjecture was firstly confirmed for $p>Cn^{-1/2}$ for a large constant C>0 by Fountoulakis\, Kang and Makai. Although this result has been reproved recently by Tran and Vu and by Berkowitz and Devlin\, none of them managed to extend it beyond the barrier $p>Cn^{-1/2}$. We prove the conjecture for sparser random graphs G(n\,p)\, where $Dn^{-3/5}\log n < p < C n^{-1/2}$ with a large constant D>0. \nJoint work with Debsoumya Chakraborti\, Jeong Han Kim and Tuan Tran. \nHong Liu\, Sublinear expanders and its applications\nI will review the history of sublinear expander and present some recent applications\, which lead to resolutions of several long-standing problems in sparse graphs embeddings. \nJinyoung Park (박진영)\, The threshold for the square of a Hamilton cycle\nWe will talk about a recent result of Jeff Kahn\, Bhargav Narayanan\, and myself stating that the threshold for the random graph G(n\,p) to contain the square of a Hamilton cycle is $1/\sqrt n$\, resolving a conjecture of Kühn and Osthus from 2012. The proof idea is motivated by the recent work of Frankston and the three aforementioned authors on a conjecture of Talagrand — “a fractional version of Kahn-Kalai expectation threshold conjecture.”
URL:https://dimag.ibs.re.kr/event/2021-04-30/
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210427T163000
DTEND;TZID=Asia/Seoul:20210427T173000
DTSTAMP:20260418T034111
CREATED:20210419T130854Z
LAST-MODIFIED:20240705T185048Z
UID:3961-1619541000-1619544600@dimag.ibs.re.kr
SUMMARY:Jungho Ahn (안정호)\, Well-partitioned chordal graphs with the obstruction set and applications
DESCRIPTION:We introduce a new subclass of chordal graphs that generalizes split graphs\, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star structure\, the leaves of which are of size one. Well-partitioned chordal graphs are a generalization of this concept in the following two ways. First\, the cliques in the partition can be arranged in a tree structure\, and second\, each clique is of arbitrary size. We mainly provide a characterization of well-partitioned chordal graphs by forbidden induced subgraphs and give a polynomial-time algorithm that given any graph\, either finds an obstruction or outputs a partition of its vertex set that asserts that the graph is well-partitioned chordal. We demonstrate the algorithmic use of this graph class by showing that two variants of the problem of finding pairwise disjoint paths between k given pairs of vertices are in FPT\, parameterized by k\, on well-partitioned chordal graphs\, while on chordal graphs\, these problems are only known to be in XP. From the other end\, we introduce some problems that are polynomial-time solvable on split graphs but become NP-complete on well-partitioned chordal graphs. \nThis is joint work with Lars Jaffke\, O-joung Kwon\, and Paloma T. Lima.
URL:https://dimag.ibs.re.kr/event/2021-04-27/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210421T170000
DTEND;TZID=Asia/Seoul:20210421T180000
DTSTAMP:20260418T034111
CREATED:20210414T142646Z
LAST-MODIFIED:20240705T185049Z
UID:3936-1619024400-1619028000@dimag.ibs.re.kr
SUMMARY:Reinhard Diestel\, Tangles of set separations: a novel clustering method and type recognition in machine learning
DESCRIPTION:Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that typically occur together. They can thereby discover\, relate\, and structure types: of behaviour\, political views\, texts\, or proteins. Tangles offer a new\, quantitative\, paradigm for grouping phenomena rather than things. They can identify key phenomena that allow predictions of others. Tangles also offer a new paradigm for clustering in large data sets.  \nThe mathematical theory of tangles has its origins in the theory of graph minors developed by Robertson and Seymour. It has recently been axiomatized in a way that makes it applicable to a wide range of contexts outside mathematics: from clustering in data science to predicting customer behaviour in economics\, from DNA sequencing and drug development to text analysis and machine learning. \nThis very informal talk will not show you the latest intricacies of abstract tangle theory (for which you can find links on the tangle pages of my website)\, but to win you over to join our drive to develop real tangle applications in areas as indicated above. We have some software to share\, but are looking for people to try it out with us on real-world examples! \nHere are some introductory pages from a book I am writing on this\, which may serve as an extended abstract: https://arxiv.org/abs/2006.01830
URL:https://dimag.ibs.re.kr/event/2021-04-21/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210420T163000
DTEND;TZID=Asia/Seoul:20210420T173000
DTSTAMP:20260418T034111
CREATED:20210416T123209Z
LAST-MODIFIED:20240705T185049Z
UID:3946-1618936200-1618939800@dimag.ibs.re.kr
SUMMARY:Sang-il Oum (엄상일)\, What is an isotropic system?
DESCRIPTION:Bouchet introduced isotropic systems in 1983 unifying some combinatorial features of binary matroids and 4-regular graphs. The concept of isotropic system is a useful tool to study vertex-minors of graphs and yet it is not well  known. I will give an introduction to isotropic systems.
URL:https://dimag.ibs.re.kr/event/2021-04-20/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210414T170000
DTEND;TZID=Asia/Seoul:20210414T180000
DTSTAMP:20260418T034111
CREATED:20210301T235620Z
LAST-MODIFIED:20240707T081558Z
UID:3698-1618419600-1618423200@dimag.ibs.re.kr
SUMMARY:István Tomon\, Ramsey properties of semilinear graphs
DESCRIPTION:A graph $G$ is semilinear of bounded complexity if the vertices of $G$ are elements of $\mathbb{R}^{d}$\, and the edges of $G$ are defined by the sign patterns of $t$ linear functions\, where $d$ and $t$ are constants. In this talk\, I will present several results about the symmetric and asymmetric Ramsey properties of semilinear graphs. Some interesting instances of such graphs are intersection graphs of boxes\, interval overlap graphs\, and shift graphs\, so our results extend several well known theorems about the Ramsey and coloring properties of these geometrically defined graphs.
URL:https://dimag.ibs.re.kr/event/2021-04-14/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210413T163000
DTEND;TZID=Asia/Seoul:20210413T173000
DTSTAMP:20260418T034111
CREATED:20210329T063026Z
LAST-MODIFIED:20240705T190013Z
UID:3866-1618331400-1618335000@dimag.ibs.re.kr
SUMMARY:William Overman\, Some Ordered Ramsey Numbers of Graphs on Four Vertices
DESCRIPTION:Ordered Ramsey numbers were introduced in 2014 by Conlon\, Fox\, Lee\, and Sudakov. Their results included upper bounds for general graphs and lower bounds showing separation from classical Ramsey numbers. We show the first nontrivial results for ordered Ramsey numbers of specific small graphs. In particular we prove upper bounds for orderings of graphs on four vertices\, and determine some numbers exactly using  SAT solvers for lower bounds. These results are in the spirit of exact calculations for classical Ramsey numbers and use only elementary combinatorial arguments. \nThis is joint work with Jeremy Alm\, Kayla Coffey\, and Carolyn Langhoff.
URL:https://dimag.ibs.re.kr/event/2021-04-13/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210407T170000
DTEND;TZID=Asia/Seoul:20210407T180000
DTSTAMP:20260418T034111
CREATED:20210301T235812Z
LAST-MODIFIED:20240705T190042Z
UID:3701-1617814800-1617818400@dimag.ibs.re.kr
SUMMARY:Michał Pilipczuk\, Structural properties of powers of sparse graphs
DESCRIPTION:For a graph G and an integer d\, the dth power of G is the graph $G^d$ on the same vertex set as G where two vertices are considered adjacent if and only if they are at distance at most d in G. Assuming that G is sparse\, what can we say about the structure in $G^d$? Certainly $G^d$ can be dense\, as the square of a star is a complete graph\, but $G^d$ still retains many properties that can be derived from the sparsity of G. We will present some recent results in this spirit\, in particular connected to colorings and to the Erdős-Hajnal property\, assuming that G is drawn from a fixed class of bounded expansion or from a fixed nowhere dense class. The talk will be based on the recent papers: “Clustering Powers of Sparse Graphs” (with J. Nešetřil\, P. Ossona de Mendez\, and X. Zhu) and “Erdős-Hajnal properties for powers of sparse graphs” (with M. Briański\, P. Micek\, and M. Seweryn).
URL:https://dimag.ibs.re.kr/event/2021-04-07/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210406T163000
DTEND;TZID=Asia/Seoul:20210406T173000
DTSTAMP:20260418T034111
CREATED:20210308T061306Z
LAST-MODIFIED:20240705T190041Z
UID:3731-1617726600-1617730200@dimag.ibs.re.kr
SUMMARY:Rutger Campbell\, Matroid orientability and representability
DESCRIPTION:In this talk we will have a brief introduction to oriented matroids and their relation to real-representability.
URL:https://dimag.ibs.re.kr/event/2021-04-06/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210401T100000
DTEND;TZID=Asia/Seoul:20210401T110000
DTSTAMP:20260418T034111
CREATED:20210218T001134Z
LAST-MODIFIED:20240705T191014Z
UID:3642-1617271200-1617274800@dimag.ibs.re.kr
SUMMARY:Sophie Spirkl\, Pure pairs in ordered graphs
DESCRIPTION:A pure pair in a graph G is a pair of subsets A\, B of the vertex set of G such that in G\, either all of the edges or none of the edges between A and B are present. Pure pairs have been studied recently motivated by their connections to the Erdos-Hajnal conjecture. \nIn this talk\, I will discuss the topic of pure pairs in ordered graphs\, that is\, graphs with a linear ordering on their vertex set. If we exclude a graph H as an ordered induced subgraph\, how large a pure pair can we guarantee? I will talk about how the answer differs from the case of unordered graphs and show some of the techniques used. \nBased on joint work with Maria Chudnovsky\, Jacob Fox\, Alex Scott\, and Paul Seymour.
URL:https://dimag.ibs.re.kr/event/2021-04-01/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210330T163000
DTEND;TZID=Asia/Seoul:20210330T173000
DTSTAMP:20260418T034111
CREATED:20210225T090612Z
LAST-MODIFIED:20240707T081638Z
UID:3676-1617121800-1617125400@dimag.ibs.re.kr
SUMMARY:Casey Tompkins\, 3-uniform hypergraphs avoiding a cycle of length four
DESCRIPTION:We show that that the maximum number of of edges in a $3$-uniform hypergraph without a Berge-cycle of length four is at most $(1+o(1)) \frac{n^{3/2}}{\sqrt{10}}$. This improves earlier estimates by Győri and Lemons and by Füredi and Özkahya. Joint work with Ergemlidze\, Győri\, Methuku\, Salia.
URL:https://dimag.ibs.re.kr/event/2021-03-30/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210324T170000
DTEND;TZID=Asia/Seoul:20210324T180000
DTSTAMP:20260418T034111
CREATED:20210219T024236Z
LAST-MODIFIED:20240705T191012Z
UID:3649-1616605200-1616608800@dimag.ibs.re.kr
SUMMARY:Édouard Bonnet\, Twin-width and ordered binary structures
DESCRIPTION:The twin-width of a graph G can be defined as the least integer d such that there is a sequence of length |V(G)| of (strictly) coarser and coarser partitions of its vertex set V(G)\, and every part X of every partition P of the sequence has at most d other parts Y of P with both at least one edge and at least one non-edge between X and Y.  Twin-width is closely tied to total orders on the vertices\, and can be extended to general binary structures. We will thus consider the twin-width of ordered binary structures\, or if you prefer\, matrices on a finite alphabet. This turns out to be key in understanding combinatorial\, algorithmic\, and model-theoretic properties of (hereditary) classes of those objects. We will see several characterizations of bounded twin-width for these classes. The main consequences in the three domains read as follows. \n\nEnumerative combinatorics: All the classes of 0\,1-matrices with superexponential growth have growth at least n! (in turn resolving a conjecture of Balogh\, Bollobás\, and Morris on the growth of hereditary classes of ordered graphs).\nAlgorithms: First-order model checking of ordered binary structures is tractable exactly when the twin-width is bounded.\nFinite model theory: Monadically-dependent and dependent hereditary classes of ordered binary structures are the same.\n\nIn addition we get a fixed-parameter algorithm approximating matrix twin-width within a function of the optimum\, which is still missing for unordered graphs. \nJoint work with Ugo Giocanti\, Patrice Ossona de Mendez\, and Stéphan Thomassé. Similar results have been obtained independently by Pierre Simon and Szymon Toruńczyk.
URL:https://dimag.ibs.re.kr/event/2021-03-24/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210322T163000
DTEND;TZID=Asia/Seoul:20210322T173000
DTSTAMP:20260418T034111
CREATED:20210307T042041Z
LAST-MODIFIED:20240705T190041Z
UID:3721-1616430600-1616434200@dimag.ibs.re.kr
SUMMARY:Hong Liu (刘鸿)\, Nested cycles with no geometric crossing
DESCRIPTION:In 1975\, Erdős asked the following question: what is the smallest function $f(n)$ for which all graphs with $n$ vertices and $f(n)$ edges contain two edge-disjoint cycles $C_1$ and $C_2$\, such that the vertex set of $C_2$ is a subset of the vertex set of $C_1$ and their cyclic orderings of the vertices respect each other? We prove the optimal linear bound $f(n)=O(n)$ using sublinear expanders. \nThis is joint work with Irene Gil Fernández\, Jaehoon Kim and Younjin Kim.
URL:https://dimag.ibs.re.kr/event/2021-03-22/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210317T170000
DTEND;TZID=Asia/Seoul:20210317T180000
DTSTAMP:20260418T034111
CREATED:20210228T115822Z
LAST-MODIFIED:20240705T190042Z
UID:3692-1616000400-1616004000@dimag.ibs.re.kr
SUMMARY:Yixin Cao (操宜新)\, Recognizing (unit) interval graphs by zigzag graph searches
DESCRIPTION:Corneil\, Olariu\, and Stewart [SODA 1998; SIAM Journal on Discrete Mathematics 2009] presented a recognition algorithm for interval graphs by six graph searches. Li and Wu [Discrete Mathematics & Theoretical Computer Science 2014] simplified it to only four. The great simplicity of the latter algorithm is however eclipsed by the complicated and long proofs. The main purpose of this paper is to present a new and significantly shorter proof for Li and Wu’s algorithm\, as well as a simpler implementation. We also give a self-contained presentation of the recognition algorithm of Corneil [Discrete Applied Mathematics 2004] for unit interval graphs\, based on three sweeps of graph searches. Moreover\, we show that two sweeps are already sufficient. Toward the proofs of the main results\, we make several new structural observations that might be of independent interests.
URL:https://dimag.ibs.re.kr/event/2021-03-17/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210316T163000
DTEND;TZID=Asia/Seoul:20210316T173000
DTSTAMP:20260418T034111
CREATED:20210304T000046Z
LAST-MODIFIED:20240705T190041Z
UID:3717-1615912200-1615915800@dimag.ibs.re.kr
SUMMARY:Se-Young Yun (윤세영)\, Regret in Online Recommendation Systems
DESCRIPTION:We propose a theoretical analysis of recommendation systems in an online setting\, where items are sequentially recommended to users over time. In each round\, a user\, randomly picked from a population of m users\, requests a recommendation. The decision-maker observes the user and selects an item from a catalogue of n items. Importantly\, an item cannot be recommended twice to the same user. The probabilities that a user likes each item are unknown. The performance of the recommendation algorithm is captured through its regret\, considering as a reference an Oracle algorithm aware of these probabilities. We investigate various structural assumptions on these probabilities: we derive for each structure regret lower bounds\, and devise algorithms achieving these limits. Interestingly\, our analysis reveals the relative weights of the different components of regret: the component due to the constraint of not presenting the same item twice to the same user\, that due to learning the chances users like items\, and finally that arising when learning the underlying structure. \nThis is joint work with Kaito Ariu\, Narae Ryu\, and Alexandre Proutière.
URL:https://dimag.ibs.re.kr/event/2021-03-16/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210309T163000
DTEND;TZID=Asia/Seoul:20210309T173000
DTSTAMP:20260418T034111
CREATED:20210225T090525Z
LAST-MODIFIED:20240707T081706Z
UID:3674-1615307400-1615311000@dimag.ibs.re.kr
SUMMARY:Debsoumya Chakraborti\, Some classical problems in graph saturation
DESCRIPTION:Graph saturation is one of the oldest areas of investigation in extremal combinatorics. A graph $G$ is called $F$-saturated if $G$ does not contain a subgraph isomorphic to $F$\, but the addition of any edge creates a copy of $F$. The function $\operatorname{sat}(n\,F)$ is defined to be the minimum number of edges in an $n$-vertex $F$-saturated graph. \nIn the first half of the talk\, we will discuss a generalization of Erdős-Hajnal-Moon theorem (1964)\, which determined the value of $\operatorname{sat}(n\,K_s)$. We resolve one of the fundamental questions of minimizing the number of cliques of size $r$ in a $K_s$-saturated graph for all sufficiently large number of vertices\, confirming a conjecture of Kritschgau\, Methuku\, Tait\, and Timmons. We further establish a corresponding stability result. \nIn the second half\, we will focus on a central conjecture in graph saturation made by Tuza (1986)\, which states that for every graph $F$\, the limit $\lim_{n \rightarrow \infty} \frac{\operatorname{sat}(n\,F)}{n}$ exists. We make progress in the negative direction of this conjecture. \nThis talk will be based on a joint work with Po-Shen Loh.
URL:https://dimag.ibs.re.kr/event/2021-03-09/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210302T163000
DTEND;TZID=Asia/Seoul:20210302T173000
DTSTAMP:20260418T034111
CREATED:20210217T044249Z
LAST-MODIFIED:20240707T081721Z
UID:3639-1614702600-1614706200@dimag.ibs.re.kr
SUMMARY:Kevin Hendrey\, A unified half-integral Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups
DESCRIPTION:Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold if we restrict to odd cycles.  However\, in 1999\, Reed proved an analogue for odd cycles by relaxing packing to half-integral packing. We prove a far-reaching generalisation of the theorem of Reed; if the edges of a graph are labelled by finitely many abelian groups\, then there is a duality between the maximum size of a half-integral packing of cycles whose values avoid a fixed finite set for each abelian group and the minimum size of a vertex set hitting all such cycles. \nA multitude of natural properties of cycles can be encoded in this setting\, for example cycles of length at least $\ell$\, cycles of length $p$ modulo $q$\, cycles intersecting a prescribed set of vertices at least $t$ times\, and cycles contained in given $\mathbb{Z}_2$-homology classes in a graph embedded on a fixed surface. Our main result allows us to prove a duality theorem for cycles satisfying a fixed set of finitely many such properties. \nThis is joint work with J. Pascal Gollin\, Ken-ichi Kawarabayashi\, O-joung Kwon\, and Sang-il Oum.
URL:https://dimag.ibs.re.kr/event/2021-03-02/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210223T163000
DTEND;TZID=Asia/Seoul:20210223T173000
DTSTAMP:20260418T034111
CREATED:20210217T043908Z
LAST-MODIFIED:20240707T081835Z
UID:3637-1614097800-1614101400@dimag.ibs.re.kr
SUMMARY:Minki Kim (김민기)\, Rainbow paths and rainbow matchings
DESCRIPTION:We prove that if $n \geq 3$\, then any family of $3n-3$ sets of matchings of size $n$ in any graph has a rainbow matching of size $n$. This improves on a previous result\, in which $3n-3$ is replaced by $3n-2$. We also prove a “cooperative” generalization: for $t > 0$ and $n \geq 3$\, any $3n-4+t$ sets of edges\, the union of every $t$ of which contains a matching of size $n$\, have rainbow matching of size $n$. This is joint work with Ron Aharoni\, Joseph Briggs\, and Jinha Kim.
URL:https://dimag.ibs.re.kr/event/2021-02-23/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210217T100000
DTEND;TZID=Asia/Seoul:20210217T110000
DTSTAMP:20260418T034111
CREATED:20201231T022333Z
LAST-MODIFIED:20240707T081843Z
UID:3423-1613556000-1613559600@dimag.ibs.re.kr
SUMMARY:David Wood\, Tree densities of sparse graph classes
DESCRIPTION:This talk considers the following question at the intersection of extremal and structural graph theory: What is the maximum number of copies of a fixed forest $T$ in an $n$-vertex graph in a graph class $\mathcal{G}$ as $n\to \infty$? I will answer this question for a variety of sparse graph classes $\mathcal{G}$. In particular\, we show that the answer is $\Theta(n^{\alpha_d(T)})$ where $\alpha_d(T)$ is the size of the largest stable set in the subforest of $T$ induced by the vertices of degree at most $d$\, for some integer $d$ that depends on $\mathcal{G}$. For example\, when $\mathcal{G}$ is the class of $k$-degenerate graphs then $d=k$; when $\mathcal{G}$ is the class of graphs containing no $K_{s\,t}$-minor ($t\geq s$) then $d=s-1$; and when $\mathcal{G}$ is the class of $k$-planar graphs then $d=2$. All these results are in fact consequences of a single lemma in terms of a finite set of excluded subgraphs. This is joint work with Tony Huynh (arXiv:2009.12989).
URL:https://dimag.ibs.re.kr/event/2021-02-17/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210216T163000
DTEND;TZID=Asia/Seoul:20210216T173000
DTSTAMP:20260418T034111
CREATED:20210205T012237Z
LAST-MODIFIED:20240705T191023Z
UID:3594-1613493000-1613496600@dimag.ibs.re.kr
SUMMARY:Martin Ziegler\, Quantitative Coding and Complexity Theory of Continuous Data
DESCRIPTION:Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices\, characters as integers\, integers as bit strings\, and vice versa. For such discrete data\, the actual encoding is usually straightforward and/or complexity-theoretically inessential (up to polynomial time\, say). \nBut concerning continuous data\, already real numbers naturally suggest various encodings with very different computational properties. \nWe recall the existing qualitative theory of computably ‘sensible’ encodings of topological spaces; and we newly develop the quantitative theory of complexity-theoretically ‘sensible’ encodings of metric spaces. \nJoint work with Donghyun Lim.
URL:https://dimag.ibs.re.kr/event/2021-02-16/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210210T163000
DTEND;TZID=Asia/Seoul:20210210T173000
DTSTAMP:20260418T034111
CREATED:20201231T073729Z
LAST-MODIFIED:20240705T191150Z
UID:3428-1612974600-1612978200@dimag.ibs.re.kr
SUMMARY:Jie Ma (马杰)\, Non-repeated cycle lengths and Sidon sequences
DESCRIPTION:We prove a conjecture of Boros\, Caro\, Furedi and Yuster on the maximum number of edges in a 2-connected graph without repeated cycle lengths\, which is a restricted version of a longstanding problem of Erdos. Our proof together with the matched lower bound construction of Boros\, Caro\, Furedi and Yuster show that this problem can be conceptually reduced to the seminal problem of finding the maximum Sidon sequences in number theory. Joint work with Tianchi Yang.
URL:https://dimag.ibs.re.kr/event/2021-02-10/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210209T163000
DTEND;TZID=Asia/Seoul:20210209T173000
DTSTAMP:20260418T034111
CREATED:20210203T050722Z
LAST-MODIFIED:20240705T191023Z
UID:3581-1612888200-1612891800@dimag.ibs.re.kr
SUMMARY:Doowon Koh (고두원)\, On the cone restriction conjecture in four dimensions and applications in incidence geometry
DESCRIPTION:Main purpose of this talk is to introduce a connection between restriction estimates for cones and point-sphere incidence theorems in the finite field setting. First\, we review the finite field restriction problem for cones and address new results on the conical restriction problems. In particular\, we establish the restriction conjecture for the cone in four dimensions. Second\, we study how to apply the conical restriction results to the point-sphere incidence bounds. As a consequence\, we obtain sharp point-sphere incidence bounds when sphere sets are not too big.
URL:https://dimag.ibs.re.kr/event/2021-02-09/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210203T163000
DTEND;TZID=Asia/Seoul:20210203T173000
DTSTAMP:20260418T034111
CREATED:20201106T054235Z
LAST-MODIFIED:20240705T193028Z
UID:3241-1612369800-1612373400@dimag.ibs.re.kr
SUMMARY:Ron Aharoni\, Colorful KKM and multiple cakes division
DESCRIPTION:In the “cake partition” problem n players have each a list of preferred parts for any partition of the [0\,1] interval (“cake”) into n sub-intervals. Woodall\, Stromquist and Gale proved independently that under mild conditions on the list of preferences (like continuity) there is always a partition and assignment of parts to the players\, in which every player gets a piece belonging to her list of preferred parts. In fact\, Gale proved a colorful version of the famous KKM theorem\, not realizing that this is the same problem\, but on the other hand\, proved the problem its proper setting. I will discuss the case of partitioning more than one cake – how many players can you make happy\, when there is a general number of cakes\, and general number of players. \nJoint work with Eli Berger\, Joseph Briggs\, Erel Segal-Halevi and Shira Zerbib.
URL:https://dimag.ibs.re.kr/event/2021-02-03/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210127T100000
DTEND;TZID=Asia/Seoul:20210127T110000
DTSTAMP:20260418T034111
CREATED:20210114T124234Z
LAST-MODIFIED:20240705T191135Z
UID:3500-1611741600-1611745200@dimag.ibs.re.kr
SUMMARY:Dong Yeap Kang (강동엽)\, A proof of the Erdős-Faber-Lovász conjecture
DESCRIPTION:A hypergraph is linear if every pair of two distinct edges shares at most one vertex. A longstanding conjecture by Erdős\, Faber\, and Lovász in 1972\, states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. \nIn this talk\, I will present the ideas to prove the conjecture for all large $n$. This is joint work with Tom Kelly\, Daniela Kühn\, Abhishek Methuku\, and Deryk Osthus.
URL:https://dimag.ibs.re.kr/event/2021-01-27/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210126T043000
DTEND;TZID=Asia/Seoul:20210126T173000
DTSTAMP:20260418T034111
CREATED:20210125T042312Z
LAST-MODIFIED:20240707T081932Z
UID:3545-1611635400-1611682200@dimag.ibs.re.kr
SUMMARY:Tuan Tran\, Minimum saturated families of sets
DESCRIPTION:A family $\mathcal F$ of subsets of [n] is called s-saturated if it contains no s pairwise disjoint sets\, and moreover\, no set can be added to $\mathcal F$ while preserving this property. More than 40 years ago\, Erdős and Kleitman conjectured that an s-saturated family of subsets of [n] has size at least $(1 – 2^{-(s-1)})2^n$. It is a simple exercise to show that every s-saturated family has size at least $2^{n-1}$\, but\, as was mentioned by Frankl and Tokushige\, even obtaining a slightly better bound of $(1/2 + \varepsilon)2^n$\, for some fixed $\varepsilon > 0$\, seems difficult. We prove such a result\, showing that every s-saturated family of subsets of [n] has size at least $(1 – 1/s)2^n$. In this talk\,  I will present two short proofs. This is joint work with M. Bucic\, S. Letzter and B. Sudakov.
URL:https://dimag.ibs.re.kr/event/2021-01-26/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210120T163000
DTEND;TZID=Asia/Seoul:20210120T173000
DTSTAMP:20260418T034111
CREATED:20201211T084524Z
LAST-MODIFIED:20240707T081951Z
UID:3358-1611160200-1611163800@dimag.ibs.re.kr
SUMMARY:Yusuke Kobayashi (小林 佑輔)\, An FPT Algorithm for Minimum Additive Spanner Problem
DESCRIPTION:For a positive integer t and a graph G\, an additive t-spanner of G is a spanning subgraph in which the distance between every pair of vertices is at most the original distance plus t. Minimum Additive t-Spanner Problem is to find an additive t-spanner with the minimum number of edges in a given graph\, which is known to be NP-hard. Since we need to care about global properties of graphs when we deal with additive t-spanners\, Minimum Additive t-Spanner Problem is hard to handle\, and hence only few results are known for it. In this talk\, we study Minimum Additive t-Spanner Problem from the viewpoint of parameterized complexity. We formulate a parameterized version of the problem in which the number of removed edges is regarded as a parameter\, and give a fixed-parameter algorithm for it. We also extend our result to (α\,β)-spanners.
URL:https://dimag.ibs.re.kr/event/2021-01-20/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210119T163000
DTEND;TZID=Asia/Seoul:20210119T173000
DTSTAMP:20260418T034111
CREATED:20210114T070412Z
LAST-MODIFIED:20240705T191136Z
UID:3498-1611073800-1611077400@dimag.ibs.re.kr
SUMMARY:Ben Lund\, Perfect matchings and derangements on graphs
DESCRIPTION:We show that each perfect matching in a bipartite graph G intersects at least half of the perfect matchings in G. This result has equivalent formulations in terms of the permanent of the adjacency matrix of a graph\, and in terms of derangements and permutations on graphs. We give several related results and open questions. This is joint work with Matija Bucic\, Pat Devlin\, Mo Hendon\, and Dru Horne.
URL:https://dimag.ibs.re.kr/event/2021-01-19/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR