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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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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:20240101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250401T163000
DTEND;TZID=Asia/Seoul:20250401T173000
DTSTAMP:20260417T000411
CREATED:20250310T023035Z
LAST-MODIFIED:20250310T023155Z
UID:10673-1743525000-1743528600@dimag.ibs.re.kr
SUMMARY:Hyunwoo Lee (이현우)\, Reconstructing hypergraph matching polynomials
DESCRIPTION:By utilizing the recently developed hypergraph analogue of Godsil’s identity by the second author\, we prove that for all $n \geq k \geq 2$\, one can reconstruct the matching polynomial of an $n$-vertex $k$-uniform hypergraph from the multiset of all induced sub-hypergraphs on $\lfloor \frac{k-1}{k}n \rfloor + 1$ vertices. This generalizes the well-known result of Godsil on graphs in 1981 to every uniform hypergraph. As a corollary\, we show that for every graph $F$\, one can reconstruct the number of $F$-factors in a graph under analogous conditions. We also constructed examples that imply the number $\lfloor \frac{k-1}{k}n \rfloor + 1$ is the best possible for all $n\geq k \geq 2$ with $n$ divisible by $k$. This is joint work Donggyu Kim.
URL:https://dimag.ibs.re.kr/event/2025-04-01/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250408T163000
DTEND;TZID=Asia/Seoul:20250408T173000
DTSTAMP:20260417T000411
CREATED:20250210T063056Z
LAST-MODIFIED:20250331T224202Z
UID:10560-1744129800-1744133400@dimag.ibs.re.kr
SUMMARY:Marcelo Garlet Milani\, Cycles of Well-Linked Sets and an Elementary Bound for the Directed Grid Theorem
DESCRIPTION:In 2015\, Kawarabayashi and Kreutzer proved the directed grid theorem. The theorem states the existence of a function f such that every digraph of directed tree-width f(k) contains a cylindrical grid of order k as a butterfly minor\, but the given function grows non-elementarily with the size of the grid minor. \nWe present an alternative proof of the directed grid theorem\, first proven by Kawarabayashi and Kreutzer in 2015\, which is conceptually much simpler\, more modular in its composition and also improves the upper bound for the function f to a power tower of height 22. \nOur proof is inspired by the breakthrough result of Chekuri and Chuzhoy\, who proved a polynomial bound for the excluded grid theorem for undirected graphs. We translate a key concept of their proof to directed graphs by introducing cycles of well-linked sets (CWS)\, and show that any digraph of high directed tree-width contains a large CWS\, which in turn contains a large cylindrical grid. \nThis is joint work with Meike Hatzel\, Stephan Kreutzer and Irene Muzi.
URL:https://dimag.ibs.re.kr/event/2025-04-08/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250414T110000
DTEND;TZID=Asia/Seoul:20250414T120000
DTSTAMP:20260417T000411
CREATED:20250218T063907Z
LAST-MODIFIED:20250318T144436Z
UID:10608-1744628400-1744632000@dimag.ibs.re.kr
SUMMARY:Daniel McGinnis\, A necessary and sufficient condition for $k$-transversals
DESCRIPTION:We solve a long-standing open problem posed by Goodman and Pollack in 1988 by establishing a necessary and sufficient condition for a finite family of convex sets in $\mathbb{R}^d$ to admit a $k$-transversal (a $k$-dimensional affine subspace that intersects each set) for any $0 \le k \le d-1$. This result is a common generalization of Helly’s theorem ($k=0$) and the Goodman-Pollack-Wenger theorem ($k=d-1$). \nThis is joint work with Nikola Sadovek.
URL:https://dimag.ibs.re.kr/event/2025-04-14/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250415T163000
DTEND;TZID=Asia/Seoul:20250415T173000
DTSTAMP:20260417T000411
CREATED:20250211T042237Z
LAST-MODIFIED:20250331T222415Z
UID:10569-1744734600-1744738200@dimag.ibs.re.kr
SUMMARY:Nicola Lorenz\, A Minor Characterisation of Normally Spanned Sets of Vertices
DESCRIPTION:A rooted spanning tree of a graph $G$ is called normal if the endvertices of all edges of $G$ are comparable in the tree order. It is well known that every finite connected graph has a normal spanning tree (also known as depth-first search tree). Also\, all countable graphs have normal spanning trees\, but uncountable complete graphs for example do not. In 2021\, Pitz proved the following characterisation for graphs with normal spanning trees\, which had been conjectured by Halin: A connected graph $G$ has a normal spanning tree if and only if every minor of $G$ has countable colouring number\, i.e. there is a well-order of the vertices such that every vertex is preceded by only finitely many of its neighbours. \nMore generally\, a not necessarily spanning tree in $G$ is called normal if for every path $P$ in $G$ with both endvertices in $T$ but no inner vertices in $T$\, the endvertices of $P$ are comparable in the tree order. We establish a local version of Pitz’s theorem by characterising for which sets $U$ of vertices of $G$ there is a normal tree in $G$ covering $U$. The results are joint work with Max Pitz.
URL:https://dimag.ibs.re.kr/event/2025-04-15/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250422T163000
DTEND;TZID=Asia/Seoul:20250422T173000
DTSTAMP:20260417T000411
CREATED:20250210T062933Z
LAST-MODIFIED:20250414T092141Z
UID:10558-1745339400-1745343000@dimag.ibs.re.kr
SUMMARY:Marcin Briański\, Burling Graphs as (almost) universal obstacles to  $\chi$-boundedness
DESCRIPTION:What causes a graph to have high chromatic number? One obvious reason is containing a large clique (a set of pairwise adjacent vertices). This naturally leads to investigation of \(\chi\)-bounded classes of graphs — classes where a large clique is essentially the only reason for large chromatic number. \nUnfortunately\, many interesting graph classes are not \(\chi\)-bounded. An eerily common obstruction to being \(\chi\)-bounded are the Burling graphs — a family of triangle-free graphs with unbounded chromatic number. These graphs have served as counterexamples in many settings: demonstrating that graphs excluding an induced subdivision of \(K_{5}\) are not \(\chi\)-bounded\, that string graphs are not \(\chi\)-bounded\, that intersection graphs of boxes in \({\mathbb{R}}^{3}\) are not \(\chi\)-bounded\, and many others. \nIn many of these cases\, this sequence is the only known obstruction to \(\chi\)-boundedness. This led Chudnovsky\, Scott\, and Seymour to conjecture that any graph of sufficiently high chromatic number must either contain a large clique\, an induced proper subdivision of a clique\, or a large Burling graph as an induced subgraph. \nThe prevailing belief was that this conjecture should be false. Somewhat surprisingly\, we did manage to prove it under an extra assumption on the “locality” of the chromatic number — that the input graph belongs to a \(2\)-controlled family of graphs\, where a high chromatic number is always certified by a ball of radius \(2\) with large chromatic number. \nIn this talk\, I will present this result and discuss its implications in structural graph theory\, and algorithmic implications to colouring problems in specific graph families. \nThis talk is based on joint work with Tara Abrishami\, James Davies\, Xiying Du\, Jana Masaříková\, Paweł Rzążewski\, and Bartosz Walczak conducted during the STWOR2 workshop in Chęciny Poland.
URL:https://dimag.ibs.re.kr/event/2025-04-22/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250428T110000
DTEND;TZID=Asia/Seoul:20250428T120000
DTSTAMP:20260417T000411
CREATED:20250417T134915Z
LAST-MODIFIED:20250418T012250Z
UID:10801-1745838000-1745841600@dimag.ibs.re.kr
SUMMARY:Pascal Schweitzer\, Recent insights surrounding combinatorial approaches to isomorphism and symmetry problems
DESCRIPTION:Modern practical software libraries that are designed for isomorphism tests and symmetry computation rely on combinatorial techniques combined with techniques from algorithmic group theory. The Weisfeiler-Leman algorithm is such a combinatorial technique. When taking a certain view from descriptive complexity theory\, the algorithm is universal. After an introduction to problems arising in symmetry computation and this particular combinatorial technique\, I will give an overview of results from recent years. The results give insights into worst-case behavior and computational complexity.
URL:https://dimag.ibs.re.kr/event/2025-04-28/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20250429T163000
DTEND;TZID=Asia/Seoul:20250429T173000
DTSTAMP:20260417T000411
CREATED:20250212T111256Z
LAST-MODIFIED:20250212T112909Z
UID:10581-1745944200-1745947800@dimag.ibs.re.kr
SUMMARY:Eunjin Oh (오은진)\, Approximation Algorithms for the Geometric Multimatching Problem
DESCRIPTION:Let S and T be two sets of points in a metric space with a total of n points. Each point in S and T has an associated value that specifies an upper limit on how many points it can be matched with from the other set. A multimatching between S and T is a way of pairing points such that each point in S is matched with at least as many points in T as its assigned value\, and vice versa for each point in T. The cost of a multimatching is defined as the sum of the distances between all matched pairs of points. The geometric multimatching problem seeks to find a multimatching that minimizes this cost. A special case where each point is matched to at most one other point is known as the geometric many-to-many matching problem. \nWe present two results for these problems when the underlying metric space has a bounded doubling dimension. Specifically\, we provide the first near-linear-time approximation scheme for the geometric multimatching problem in terms of the output size. Additionally\, we improve upon the best-known approximation algorithm for the geometric many-to-many matching problem\, previously introduced by Bandyapadhyay and Xue (SoCG 2024)\, which won the best paper award at SoCG 2024. \nThis is joint work with Shinwoo An and Jie Xue.
URL:https://dimag.ibs.re.kr/event/2025-04-29/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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