기초과학연구원 이산수학그룹
Hadwiger's famous coloring conjecture states that every t-chromatic graph contains a $K_t$-minor. Holroyd conjectured the following strengthening of Hadwiger's conjecture: If G is a t-chromatic graph and S⊆V(G) takes all …
We show fixed-parameter tractability of the Directed Multicut problem with three terminal pairs (with a randomized algorithm). This problem, given a directed graph $G$, pairs of vertices (called terminals) $(s_1,t_1)$, …
Let $X$ be a 2-dimensional simplicial complex. Denote by $\text{ex}_{\hom}(n,X)$ the maximum number of 2-simplices in an $n$-vertex simplicial complex that has no sub-simplicial complex homeomorphic to $X$. The asymptotics …
Given an undirected planar graph $G$ with $n$ vertices and a set $T$ of $k$ pairs $(s_i,t_i)_{i=1}^k$ of vertices, the goal of the planar disjoint paths problem is to find …
We give a summary on the work of the last months related to Frankl's Union-Closed conjecture and its offsprings. The initial conjecture is stated as a theorem in extremal set …
Extremal Combinatorics studies the maximum or minimum size of finite objects (numbers, sets, graphs) satisfying certain properties. In this talk, I introduce the conjectures I solved on Extremal Combinatorics, and …
In this talk, we will discuss the problem of determining the maximum number of edges in an n-vertex k-critical graph. A graph is considered k-critical if its chromatic number is …
Configurations of axis-parallel boxes in $\mathbb{R}^d$ are extensively studied in combinatorial geometry. Despite their perceived simplicity, there are many problems involving their structure that are not well understood. I will …
Pivot-minors can be thought of as a dense analogue of graph minors. We shall discuss pivot-minors and two recent results for proper pivot-minor-closed classes of graphs. In particular, that for …
For a given graph $H$, we say that a graph $G$ has a perfect $H$-subdivision tiling if $G$ contains a collection of vertex-disjoint subdivisions of $H$ covering all vertices of …