기초과학연구원 이산수학그룹
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 …
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 …
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 …
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 …
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 …
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 …
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 …