기초과학연구원 이산수학그룹
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 …
A family of sets in $$ is called an $\ell$-Oddtown if the sizes of all sets are not divisible by $\ell$, but the sizes of pairwise intersections are divisible by $\ell$. The problem was completely solved when $\ell$ is a prime via an elegant linear algebraic method, showing that the family has size at most …
Let $\alpha(\mathbb{F}_q^{d},p)$ be the maximum possible size of a point set in general position in a $p$-random subset of $\mathbb{F}_q^d$. We determine the order of magnitude of $\alpha(\mathbb{F}_q^{d},p)$ up to a polylogarithmic factor by proving the balanced supersaturation conjecture of Balogh and Luo. Our result also resolves a conjecture implicitly posed by the first author, …
The cycle double cover conjecture (CDC) claims that every graph without cut-edges has a list of cycles such that every edge appears exactly twice in the list. This conjecture was proposed in 1970s by several mathematicians independently, including Tutte, Seymour, and Szekeres. On July 10, 2026, OpenAI released a proof found by its ChatGPT 5.6 …
For $\boldsymbol{\alpha} = (\alpha_1, \dots, \alpha_k) \in {\mathbb F}_2^k$, an $\boldsymbol{\alpha} $-town is a set family in which every $i$-wise intersection has parity $\alpha_i$. Denote by $f_{\boldsymbol{\alpha} }(n)$ the maximum size of an $\boldsymbol{\alpha} $-town on $$. The classical oddtown and eventown problems study the cases $\boldsymbol{\alpha} = (1, 0)$ and $(0, 0)$, respectively. We …
Website: https://kscw.combinatorics.kr/
One of the important algorithmic consequences of Robertson and Seymour's Graph Minor Project is their proof that the k-Vertex-Disjoint Paths problem is fixed-parameter tractable on the class of all undirected graphs, that is, solvable in time $f(k) \cdot n^c$, for some function $f$ and constant $c$. For directed graphs the problem is significantly harder: the …
We study restricted-link augmentation to 2-vertex-connectivity. An instance consists of a graph $G$, possibly disconnected, a set $L$ of admissible links on its vertices, integer link costs in $\{1, \ldots, W\}$, and an integer $k$; the task is to add at most $k$ links of minimum total cost so that the resulting multigraph is 2-vertex-connected. …
The first major step towards the graph minor structure theorem by Robertson and Seymour was the grid theorem, a result describing that every graph of large treewidth contains a grid as minor. In 2014 Wollan gave a definition for a tree-like decomposition and a width parameter tree-cutwidth with respect to immersions, a different graph containment …
The 2026 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: …