Discrete Mathematics Group

Mamadou Moustapha Kanté, Strongly flip-flat classes of graphs
2026-04-07 16:30 - 17:30 (Asia/Seoul) | Room B332, IBS (기초과학연구원)
Strong flip-flatness appears to be the analogue of uniform almost-wideness in the setting of dense classes of graphs. Almost-wideness is a notion that was central in different characterisations of nowhere dense classes of graphs, and in particular the game-theoretic one. In this talk I will present the flip-flatness notions and conjectures about the characterization of strongly flip-flat graph classes. Then, I will present a proof that strongly flip-flat classes of graphs that are weakly sparse are indeed uniformly almost-wide, making a step towards their characterisation. A consequence is a characterization of strongly flip-flat graph classes with low rank-depth colourings.
This is a joint work with F. Ghasemi, J. Grange and F. Madelaine.

Xin Wei, Separating hash families with large universe
2026-04-28 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
Separating hash families are useful combinatorial structures that generalize several well-studied objects in cryptography and coding theory. Let $p_t(N, q)$ denote the maximum size of the universe for a $t$-perfect hash family of length $N$ over an alphabet of size $q$. We show that $q^{2 – o(1)} < p_t(t, q) = o(q^2)$ for all $t ge 3$, thereby resolving an open problem raised by Blackburn et al. (2008) for certain parameter ranges. Previously, this result was known only for $t = 3$ and $t = 4$. Our approach establishes the existence of a large set of integers that avoids nontrivial solutions to a system of correlated linear equations. This is joint work with Xiande Zhang and Gennian Ge.

Maximilian Gorsky, The Disjoint Paths Problem lies in the Oort cloud of algorithms
2026-05-06 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
In this talk we discuss recent work to that establishes that the bounds of the Vital Linkage Function is single-exponential. This has immediate impacts on the complexity of the k-Disjoint Paths Problem, Minor Checking, and more generally, the Folio-Problem. We in fact prove something even stronger: It turns out that it is not in fact the number of terminals (or more generally vertices) that matters in these problems, but rather their structure within the graph. Concretely, we show that the Vital Linkage Function is single-exponential only in the bidimensionality of the terminals, whilst the number of terminals contributes only polynomially. A direct consequence of this is an algorithm for the k-Disjoint Paths Problem running in $f(k)n^2$-time, where f(k) is singly exponential in k and doubly exponential in the bidimensionality of k. This derives directly from an algorithm for the Folio-problem we give that has an analogous runtime. Notably these are the first algorithms for these problems in which the function f is explicit. In particular, we give the first explicit bounds for the Vital Linkage Function.
Joint work with Dario Cavallaro, Stephan Kreutzer, Dimitrios Thilikos, and Sebastian Wiederrecht.

Benjamin Duhamel, Excluding a forest induced minor
2026-05-12 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
We give an induced counterpart of the Forest Minor theorem: for any t ≥ 2, the $K_{t,t}$-subgraph-free H-induced-minor-free graphs have bounded pathwidth if and only if H belongs to a class F of forests, which we describe as the induced minors of two (very similar) infinite parameterized families. This constitutes a significant step toward classifying the graphs H for which every weakly sparse H-induced-minor-free class has bounded treewidth. Our work builds on the theory of constellations developed in the Induced Subgraphs and Tree Decompositions series.
This is a joint work with É. Bonnet and R. Hickingbotham.

Xavier Goaoc, TBA
2026-05-19 16:30 - 17:30 | Room B332, IBS (기초과학연구원)

Sarah Morell, Unsplittable Transshipments
2026-05-26 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
We consider an arc-capacitated directed graph $D=(V,A)$, where each node $v$ is associated with a rational balance value $b(v)$. Nodes with negative balance values are referred to as sources, while those with positive balance values are called sinks. A feasible $b$-transshipment is a flow $f : A to mathbb{R}_{ge 0}$ that routes the total supply of the sources to the sinks through $D$, while respecting the given arc capacity constraints and satisfying the balance requirements at each node. An unsplittable $b$-transshipment additionally requires that, for each source-sink pair, the flow sent from that source to that sink is routed along at most one directed path. Unsplittable $b$-transshipments (UT) generalize the well-studied single source unsplittable flow (SSUF) problem in which $D$ contains a single source and multiple sinks, and each demand must be routed along a single path from the common source to its destination.
Given a feasible $b$-transshipment $f$ that is not necessarily unsplittable, a natural question is whether there exists an feasible unsplittable $b$-transshipment flow $g$ that approximates $f$ in an arc-wise sense. In particular, we seek bounds on the maximum deviation $|f_a-g_a|$ over all arcs $a in A$. For the special case of SSUFs, Dinitz, Garg, and Goemans (Combinatorica 1999) proved that there exists an unsplittable flow $g$ such that $g_a leq f_a + d_{max}$ for all $a in A$, where $d_{max}$ denotes the maximum demand value. Jointly with Martin Skutella (Mathematical Programming 2022), we studied unsplittable flows with arc-wise lower bounds and showed that there exists an unsplittable flow $g$ satisfying $g_a ge f_a – d_{max}$ for all $a in A$.
In this talk, we extend this line of research by adapting the techniques of Dinitz, Garg, and Goemans to the more general setting of UTs. We show that, given any feasible $b$-transshipment $f$, there exists a feasible unsplittable $b$-transshipment $g$ such that $g_a leq f_a + d_{max}$ (resp. $g_a ge f_a – d_{max}$) for all $a in A$.
This is joint work with Srinwanti Debgupta and Martin Skutella.

Maria Chudnovsky, TBA
2026-06-02 16:30 - 17:30 | Room B332, IBS (기초과학연구원)

Martin Milanič, TBA
2026-06-09 16:30 - 17:30 | Room B332, IBS (기초과학연구원)

2026 Workshop on Topological Combinatorics
2026-06-28 - 2026-07-11 | GIST
The 2026 Workshop on Topological Combinatorics will be held from June 28 to July 11, 2026 at Gwangju Institute of Science and Technology (GIST), located in Gwangju in the southwest of Republic of Korea.
The workshop aims to bring together researchers interested in applications of topology to combinatorics and related areas. This will be the fifth workshop in a series initiated by Ron Aharoni (August 2018 in Shantou, July 2019 in Prague, July 2020 on Zoom, and June 2024 in Paris).
The first week (June 28 – July 04) will be reserved for presentations, while the following days (July 05 – July 11) will be for discussion and collaborations.
The campus offers a variety of amenities, including a guesthouse that can accommodate approximately 20 guests.
In addition, various lodging options are available within a 15–20 minute walking distance.
We are planning to provide accommodation for all invited participants, and we are also considering offering partial travel support for those with limited funding.

Website: https://sites.google.com/view/2026topocomb

Ting-Wei Chao, Entropy method and mixture bound
2026-07-10 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
The entropy method has been used in many recent works in extremal combinatorics. With the help of Shannon entropy, significant progress has been made on several classical problems, such as the union-closed conjecture and the Sidorenko conjecture. In our recent work, we use the entropy method to give new proofs of the Kruskal–Katona theorem and Turán’s theorem, as well as some of their generalizations. The new ingredient in our approach is a method for upper bounding the sum of $2^{mathbb{H}(X_i)}$ for random variables $X_1,cdots,X_k$ whose supports do not overlap too much. We call this method the mixture bound, and it can be viewed as an entropic version of double counting. In this talk, I will introduce the mixture bound and show some examples of how it can be applied on colorful versions of the Kruskal–Katona theorem. Base on joint work with Maya Sankar and Hung-Hsun Hans Yu.

2026 Korean Student Combinatorics Workshop
2026-07-27 - 2026-07-31 | Gongju Hanok Village, Gongju
Website: https://kscw.combinatorics.kr/

Jinyoung Park (박진영), TBA
2026-08-18 16:30 - 17:30 | Room B332, IBS (기초과학연구원)
