Discrete Mathematics Group

Marcelo Sales, On the Ramsey number of Daisies and other hypergraphs
2025-09-30 16:30 - 17:30 (Asia/Seoul) | Room B332, IBS (기초과학연구원)
Given a $k$-uniform hypergraph $H$, the Ramsey number $R(H;q)$ is the smallest integer $N$ such that any $q$-coloring of the edges of the complete $k$-uniform hypergraph on $N$ vertices contains a monochromatic copy of $H$.
When $H$ is a complete hypergraph, a classical argument of Erdős, Hajnal, and Rado reduces the general problem to the case of uniformity $k = 3$. In this talk, we will survey constructions that lift Ramsey numbers to higher uniformities and discuss recent progress on quantitative bounds for $R(H;q)$ for certain families of hypergraphs.
This is joint work with Ayush Basu, Dániel Dobák, Pavel Pudlák, and Vojtěch Rödl.

Rong Luo, Modulo flows and Integer flows of signed graphs
2025-09-22 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
Nowhere-zero flows of unsigned graphs were introduced by Tutte in 1954 as a dual problem to vertex-coloring of (unsigned) planar graphs. The definition of nowhere-zero flows on signed graphs naturally comes from the study of embeddings of graphs in non-orientable surfaces, where nowhere-zero flows emerge as the dual notion to local tensions. Nowhere-zero flows in signed graphs were introduced by Edmonds and Johnson in 1970 for expressing algorithms on matchings, but systematically studied first by Bouchet in 1983. Bouchet also stated a conjecture which occupies a central place in the area of signed graphs: Every flow-admissible signed graph admits a nowhere-zero 6-flow. There is a significant difference in the flows of signed graphs and unsigned graphs. In this talk I will talk about the progress on the development of the flow theory of signed graphs.

Mujin Choi (최무진), Excluding ladder and wheel as induced minor in graphs without induced stars
2025-09-16 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
We prove that for all positive integers $k$ and $d$, the class of $K_{1,d}$-free graphs not containing the $k$-ladder or the $k$-wheel as an induced minor has a bounded tree-independence number. Our proof uses a generalization of the concept of brambles to tree-independence number. This is based on joint work with Claire Hilaire, Martin Milanič, and Sebastian Wiederrecht.

Katherine Perry, Symmetry breaking in trees
2025-09-09 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
We will discuss two symmetry breaking parameters: distinguishing number and fixing number. Despite being introduced independently, they share meaningful connections. In particular, we show that if a tree is 2-distinguishable with order at least 3, it suffices to fix at most 4/11 of the vertices and if a tree is $d$-distinguishable, $d geq 3$, it suffices to fix at most $frac{d-1}{d+1}$ of the vertices. We also characterize the $d$-distinguishable trees with radius $r$, for any $d geq 2$ and $r geq 1$.
This is joint work with Calum Buchanan, Peter Dankleman, Isabel Harris, Paul Horn, and Emily Rivett-Carnac.

Zhifei Yan, A Rainbow version of Lehel's conjecture
2025-09-02 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
Lehel’s conjecture states that every 2-edge-colouring of the complete graph $K_n$ admits a partition of its vertices into two monochromatic cycles. This was proven for sufficiently large n by Luczak, Rödl, and Szemerédi (1998), extended by Allen (2008), and fully resolved by Bessy and Thomassé in 2010.
We consider a rainbow version of Lehel’s conjecture for properly edge-coloured complete graphs. We prove that for any properly edge-coloured $K_n$ with sufficiently large n, there exists a partition of the vertex set into two rainbow cycles, each containing no two edges of the same colour.
This is joint work with Pedro Araújo, Xiaochuan Liu, Taísa Martins, Walner Mendonça, Luiz Moreira, and Vinicius Fernandes dos Santos.

Sang-il Oum (엄상일), The Erdős-Pósa property for circle graphs as vertex-minors
2025-08-29 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
We prove that for any circle graph $H$ with at least one edge and for any positive integer $k$, there exists an integer $t=t(k,H)$ so that every graph $G$ either has a vertex-minor isomorphic to the disjoint union of $k$ copies of $H$, or has a $t$-perturbation with no vertex-minor isomorphic to $H$. Using the same techniques, we also prove that for any planar multigraph $H$, every binary matroid either has a minor isomorphic to the cycle matroid of $kH$, or is a low-rank perturbation of a binary matroid with no minor isomorphic to the cycle matroid of $H$. This is joint work with Rutger Campbell, J. Pascal Gollin, Meike Hatzel, O-joung Kwon, Rose McCarty, and Sebastian Wiederrecht.

2025 Korean Student Combinatorics Workshop (KSCW2025: 2025 조합론 학생 워크샵)
2025-08-20 - 2025-08-24 | The K-Hotel Gyeongju
Venue
The K-Hotel Gyeongju
Website
https://indico.ibs.re.kr/e/kscw2025
Organizers

Seokbeom Kim (김석범), KAIST and IBS Discrete Mathematics Group
Hyunwoo Lee (이현우), KAIST and IBS Extremal Combinatorics and Probability Group
Jaehyeon Seo (서재현), Yonsei University
Kyungjin Cho (조경진), POSTECH

2025 Combinatorics Workshop (2025 조합론 학술대회)
2025-08-18 - 2025-08-20 | IBS Science Culture Center
Website: https://cw2025.combinatorics.kr
Invited Speakers

Dongsu Kim (KAIST)
Eun Jung Kim (KAIST)
O-joung Kwon (Hanyang University)
Ae Ja Lee (Pennsylvania State University)
Zhicong Lin (Shandong University)

Organizing Committee

Sang-il Oum (엄상일), IBS Discrete Mathematics Group
Jang Soo Kim (김장수), Sungkyunkwan University
Seunghyun Seo (서승현), Kangwon National University

Chien-Chung Huang, Robust Sparsification for Matroid Intersection with Applications
2025-08-12 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
The matroid intersection problem is a fundamental problem in combinatorial optimization. In this problem we are given two matroids and the goal is to find the largest common independent set in both matroids. This problem was introduced and solved by Edmonds in the 70s. The importance of matroid intersection stems from the large variety of combinatorial optimization problems it captures; well-known examples in computer science include bipartite matching and packing of spanning trees/arborescences.
In this talk, we introduce a “sparsifer” for the matroid intersection problem and use it to design algorithms for two problems closely related to streaming: a one-way communication protocol and a streaming algorithm in the random-order streaming model.
This is a joint-work with François Sellier.

Tony Huynh, Rainbow triangles and the Erdős-Hajnal problem in projective geometries
2025-08-05 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
We formulate a geometric version of the Erdős-Hajnal conjecture that applies to finite projective geometries rather than graphs. In fact, we give a natural extension of the ‘multicoloured’ version of the Erdős-Hajnal conjecture. Roughly, our conjecture states that every colouring of the points of a finite projective geometry of dimension $n$ not containing a fixed colouring of a fixed projective geometry $H$ must contain a subspace of dimension polynomial in $n$ avoiding some colour.
When $H$ is a ‘triangle’, there are three different colourings, all of which we resolve. We handle the case that $H$ is a ‘rainbow’ triangle by proving that rainbow-triangle-free colourings of projective geometries are exactly those that admit a certain decomposition into two-coloured pieces. This is closely analogous to a theorem of Gallai on rainbow-triangle-free coloured complete graphs. The two non-rainbow colourings of $H$ are handled via a recent breakthrough result in additive combinatorics due to Kelley and Meka.
This is joint work with Carolyn Chun, James Dylan Douthitt, Wayne Ge, Matthew E. Kroeker, and Peter Nelson.

Colin Geniet, Merge-width
2025-07-29 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
This talk is an introduction to the recent notion of merge-width, proposed by Jan Dreier and Szymon Torúnczyk. I will give an overview of the context and motivations for merge-width, namely the first-order model checking problem, and present the definition, some examples, and some basic proof techniques with the example of χ-boundedness.
This is based on joint work with Marthe Bonamy.

Linda Cook, A tight algorithmic meta-theorem for distributed certification within bounded treewidth graphs
2025-07-22 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
A local certification of a graph property is a protocol in which nodes are given “certificates of a graph property” that allow the nodes to check whether their network has this property while only communicating with their local network. The key property of a local certification is that if certificates are corrupted, some node in the network will be able to recognize this. Inspired by practical concerns, the aim in LOCAL certification is to minimize the maximum size of a certificate.
In this talk we introduce local certification and open problems in the area and present some recent joint work with Eunjung Kim and Tomáš Masařík, A Tight Meta-theorem for LOCAL Certification of MSO2 Properties within Bounded Treewidth Graphs.
In this work, instead of considering a specific graph property and developing a local certification protocol tailor-made for this property, we aim for generic protocols that can certify any property expressible in a certain logical framework. We consider Monadic Second Order Logic (MSO$_2$), a powerful framework that can express properties such as non-$k$-colorability, Hamiltonicity, and $H$-minor-freeness. Unfortunately, in general, there are MSO$_2$-expressible properties that cannot be certified without huge certificates. For instance, non-3-colorability requires certificates of size $Omega(n^2/log n)$ on general $n$-vertex graphs (Göös, Suomela 2016). Hence, we impose additional structural restrictions on the graph. Inspired by their importance in centralized computing and Robertson-Seymour Graph Minor theory, we consider graphs of bounded treewidth. We provide a local certification protocol for certifying any MSO$_2$-expressible property on graphs of bounded treewidth and, consequently, a local certification protocol for certifying bounded treewidth. That is, for each integer $k$ and each MSO$_2$-expressible property $Pi$, we give a local certification protocol to certify that a graph satisfies $Pi$ and has treewidth at most $k$ using certificates of size $mathcal{O}(log n)$ (which is asymptotically optimal). Our result improves upon the works of Fraigniaud, Montealegre, Rapaport, and Todinca (Algorithmica 2024), Bousquet, Feuilloley, Pierron (PODC 2022), and the very recent work of Baterisna and Chang (PODC 2025).

2025 Summer School on Combinatorics and Algorithms (2025 조합론 및 알고리즘 여름학교)
2025-07-14 14:00 - 2025-07-18 17:00 | POSTECH, Pohang, Korea
The 2025 Summer School on Combinatorics and Algorithms is a venue for students and early-career researchers to learn selected topics in theoretical computer science and discrete mathematics. It will be a great opportunity for young and aspiring researchers to study topics which are important but not covered during the lectures in the university classes.
Website: https://combialgo.dimag.kr/
Lecturers and Topics

Édouard Bonnet, LIP, CNRS.

Induced Subgraphs and Induced Minors of Graphs

Michał Pilipczuk, University of Warsaw.

Structural Theory of Sparse Graphs

Schedule

Start on 14 July 2025 Monday, 2 PM
End on 18 July 2025 Friday, 5 PM

Mihyun Kang (강미현), Phase transitions in a random subgraph of the hypercube
2025-07-08 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
We will discuss classical and recent results about phase transitions in random subgraphs of the hypercube and beyond. The focus will be on the giant component, long cycles, large matchings, and isoperimetric properties.

Sergey Norin, Asymptotic dimension of intersection graphs
2025-07-01 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
The notion of asymptotic dimension of metric spaces, introduced by Gromov, describes their large-scale behaviour. Asymptotic dimension of graph families has been recently studied, in particular, by Bonamy et al. who proved that the asymptotic dimension of proper minor-closed graph families is at most two.
We will discuss nerve-type theorems for asymptotic dimension. In particular, we show that the asymptotic dimension of intersection graphs of balls and spheres in $mathbb{R}^d$ is at most $d+1$.
Based on joint work with Zdeněk Dvořák and with Chun-Hung Liu.

Roohani Sharma, Uniform and Constructive Polynomial Kernel for Deletion to $K_{2,p}$ Minor-Free Graphs
2025-06-25 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
Let $mathcal F$ be a fixed, finite family of graphs. In the $mathcal F$-Deletion problem, the input is a graph G and a positive integer k, and the goal is to determine if there exists a set of at most k vertices whose deletion results in a graph that does not contain any graph of $mathcal F$ as a minor. The $mathcal F$-Deletion problem encapsulates a large class of natural and interesting graph problems like Vertex Cover, Feedback Vertex Set, Treewidth-$eta$ Deletion, Treedepth-$eta$ Deletion, Pathwidth-$eta$ Deletion, Outerplanar Deletion, Vertex Planarization and many more. We study the $mathcal F$-Deletion problem from the kernelization perspective.
In a seminal work, Fomin, Lokshtanov, Misra & Saurabh [FOCS 2012] gave a polynomial kernel for this problem when the family F contains at least one planar graph. The asymptotic growth of the size of the kernel is not uniform with respect to the family $mathcal F$: that is, the size of the kernel is $k^{f(mathcal F)}$, for some function f that depends only on $mathcal F$. Also the size of the kernel depends on non-constructive constants.
Later Giannopoulou, Jansen, Lokshtanov & Saurabh [TALG 2017] showed that the non-uniformity in the kernel size bound of Fomin et al. is unavoidable as Treewidth-$eta$ Deletion, cannot admit a kernel of size $O(k^{(eta +1)/2 -epsilon)}$, for any $epsilon >0$, unless NP $subseteq$ coNP/poly. On the other hand it was also shown that Treedepth-$eta$ Deletion, admits a uniform kernel of size $f(mathcal F) k^6$, showcasing that there are subclasses of $mathcal F$ where the asymptotic kernel sizes do not grow as a function of the family $mathcal F$. This work leads to the natural question of determining classes of $mathcal F$ where the problem admits uniform polynomial kernels.
In this work, we show that if all the graphs in $mathcal F$ are connected and $mathcal F$ contains $K_{2,p}$ (a bipartite graph with 2 vertices on one side and p vertices on the other), then the problem admits a uniform kernel of size $f(mathcal F) k^{10}$ where the constants in the size bound are also constructive. The graph $K_{2,p}$ is one natural extension of the graph $theta_p$, where $theta_p$ is a graph on two vertices and p parallel edges. The case when $mathcal F$ contains $theta_p$ has been studied earlier and serves as (the only) other example where the problem admits a uniform polynomial kernel.
This is joint work with William Lochet.

Attila Jung, The Quantitative Fractional Helly Theorem
2025-06-17 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
Two celebrated extensions of Helly’s theorem are the Fractional Helly theorem of Katchalski and Liu (1979) and the Quantitative Volume theorem of Barany, Katchalski, and Pach (1982). Improving on several recent works, we prove an optimal combination of these two results. We show that given a family $F$ of $n$ convex sets in $mathbb{R}^d$ such that at least $alpha binom{n}{d+1}$ of the $(d+1)$-tuples of $F$ have an intersection of volume at least 1, then one can select $Omega_{d,alpha}(n)$ members of $F$ whose intersection has volume at least $Omega_d(1)$. Joint work with Nora Frankl and Istvan Tomon.

On-Hei Solomon Lo, Minors of non-hamiltonian graphs
2025-06-10 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
A seminal result of Tutte asserts that every 4-connected planar graph is hamiltonian. By Wagner’s theorem, Tutte’s result can be restated as: every 4-connected graph with no $K_{3,3}$ minor is hamiltonian. In 2018, Ding and Marshall posed the problem of characterizing the minor-minimal 3-connected non-hamiltonian graphs. They conjectured that every 3-connected non-hamiltonian graph contains a minor of $K_{3,4}$, $mathfrak{Q}^+$, or the Herschel graph, where $mathfrak{Q}^+$ is obtained from the cube by adding a new vertex and connecting it to three vertices that share a common neighbor in the cube. We recently resolved this conjecture along with some related problems. In this talk, we review the background and discuss the proof.

Denys Bulavka, Strict Erdős-Ko-Rado Theorems for Simplicial Complexes
2025-06-04 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
The now classical theorem of Erdős, Ko and Rado establishes
the size of a maximal uniform family of pairwise-intersecting sets as well as a characterization of the families attaining such upper bound. One natural extension of this theorem is that of restricting the possiblechoices for the sets. That is, given a simplicial complex, what is the size of a maximal uniform family of pairwise-intersecting faces. Holroyd and Talbot, and Borg conjectured that the same phenomena as in the classical case (i.e., the simplex) occurs: there is a maximal size pairwise-intersecting family with all its faces having some common vertex. Under stronger hypothesis, they also conjectured that if a family attains such bound then its members must have a common vertex. In this talk I will present some progress towards the characterization of the maximal families. Concretely I will show that the conjecture is true for near-cones of sufficiently high depth. In particular, this implies that the characterization of maximal families holds for, for example, the independence complex of a chordal graph with an isolated vertex as well as the independence complex of a (large enough) disjoint union of graphs with at least one isolated vertex. Under stronger hypothesis, i.e., more isolated vertices, we also recover a stability theorem.
This talk is based on a joint work with Russ Woodroofe.

Meike Hatzel, Counterexample to Babai's lonely colour conjecture
2025-05-27 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
Motivated by colouring minimal Cayley graphs, in 1978 Babai conjectured that no-lonely-colour graphs have bounded chromatic number. We disprove this in a strong sense by constructing graphs of arbitrarily large girth and chromatic number that have a proper edge colouring in which each cycle contains no colour exactly once.
The result presented is the joint work with James Davies and Liana Yepremyan.

Seokbeom Kim (김석범), The structure of △(1, 2, 2)-free tournaments
2025-05-13 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
Given a tournament $S$, a tournament is $S$-free if it has no subtournament isomorphic to $S$. Until now, there have been only a small number of tournaments $S$ such that the complete structure of $S$-free tournaments is known.
Let $triangle(1, 2, 2)$ be a tournament obtained from the cyclic triangle by substituting two-vertex tournaments for two of its vertices. In this talk, we present a structure theorem for $triangle(1, 2, 2)$-free tournaments, which was previously unknown. As an application, we provide tight bounds for the chromatic number as well as the size of the largest transitive subtournament for such tournaments.
This talk is based on joint work with Taite LaGrange, Mathieu Rundström, Arpan Sadhukhan, and Sophie Spirkl.

Eunjin Oh (오은진), Approximation Algorithms for the Geometric Multimatching Problem
2025-04-29 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
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.
We 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.
This is joint work with Shinwoo An and Jie Xue.

Pascal Schweitzer, Recent insights surrounding combinatorial approaches to isomorphism and symmetry problems
2025-04-28 11:00 - 12:00 | Room B332, IBS (기초과학연구원)
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.

Marcin Briański, Burling Graphs as (almost) universal obstacles to $chi$-boundedness
2025-04-22 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
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.
Unfortunately, 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.
In 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.
The 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.
In 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.
This 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.

Nicola Lorenz, A Minor Characterisation of Normally Spanned Sets of Vertices
2025-04-15 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
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.
More 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.

Daniel McGinnis, A necessary and sufficient condition for $k$-transversals
2025-04-14 11:00 - 12:00 | Room B332, IBS (기초과학연구원)
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 ($k=d-1$).
This is joint work with Nikola Sadovek.

Marcelo Garlet Milani, Cycles of Well-Linked Sets and an Elementary Bound for the Directed Grid Theorem
2025-04-08 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
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.
We 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.
Our 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.
This is joint work with Meike Hatzel, Stephan Kreutzer and Irene Muzi.

Hyunwoo Lee (이현우), Reconstructing hypergraph matching polynomials
2025-04-01 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
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 $ngeq k geq 2$ with $n$ divisible by $k$. This is joint work Donggyu Kim.

Michał Seweryn, Dimension and standard examples in planar posets
2025-03-18 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
The dimension of a poset is the least integer $d$ such that the poset is isomorphic to a subposet of the product of $d$ linear orders. In 1983, Kelly constructed planar posets of arbitrarily large dimension. Crucially, the posets in his construction involve large standard examples, the canonical structure preventing a poset from having small dimension. Kelly’s construction inspired one of the most challenging questions in dimension theory: are large standard examples unavoidable in planar posets of large dimension? We answer the question affirmatively by proving that every $d$-dimensional planar poset contains a standard example of order $Omega(d)$. More generally, we prove that every poset from Kelly’s construction appears in every poset with a planar cover graph of sufficiently large dimension.
joint work with Heather Smith Blake, Jędrzej Hodor, Piotr Micek, and William T. Trotter.

Johannes Carmesin, Open problems in graph theory
2025-03-11 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
Since the proof of the graph minor structure theorem by Robertson and Seymour in 2004, its underlying ideas have found applications in a much broader range of settings than their original context. They have driven profound progress in areas such as vertex minors, pivot minors, matroids, directed graphs, and 2-dimensional simplicial complexes. In this talk, I will present three open problems related to this development, each requiring some background.
