기초과학연구원 이산수학그룹
This talk deals with induced minor obstructions to treewidth. The natural setup for this problem is to consider the class of graphs excluding some planar graph, and some complete bipartite graph as induced minors, and some complete graph as a subgraph. Unfortunately, such classes still contain graphs of arbitrarily large treewidth. Moreover, a result of …
The grid theorem of Robertson and Seymour can be equivalently stated using balanced separators, that are separators whose deletion leaves every component with no more than half of the vertices of the graph, as follows. Every graph that excludes some planar graph as a minor has a balanced separator of bounded size. Building on this …
I will introduce a new structure on finite graphs, which takes the form of a labeling of the vertices by nonnegative integers (possibly repeated). This labeling is isomorphism invariant, and seems to reflect some mix of local and global structure of the graph. I will describe an algorithm for computing these labels, which uses a …
For a set $X$ of integer points, the relaxation complexity $\operatorname{rc}(X)$ is the smallest number of facets of any polyhedron P whose integer points are precisely those of X. In this paper, we focus on the case where X is the discrete standard simplex $\Delta_d = \{0, e_1, ..., e_d\}$. We show that $\operatorname{rc}(\Delta_d) = …
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 …
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 …