이승훈

Given a graph $G$ on the vertex set $V$, the non-matching complex of $G$, ${\mathsf{NM}}_k(G)$, is the family of subgraphs $G^{\prime }\subset G$ whose matching number $\nu (G^{\prime })$ is strictly less than $k$. As an attempt to generalize the result by Linusson, Shareshian and Welker on the homotopy types of ${\mathsf{NM}}_k(K_n)$ and ${\mathsf{NM}}_k(K_{r,s})$ to arbitrary graphs …

Motivated from the surrounding property of a point set in ${\mathbb{R}}^d$ introduced by Holmsen, Pach and Tverberg, we consider the transversal number and chromatic number of a simplicial sphere. As an attempt to give a lower bound for the maximum transversal ratio of simplicial $d$-spheres, we provide two infinite constructions. The first construction gives infinitely …

We call an order type inscribable if it is realized by a point configuration where all extreme points are all on a circle. In this talk, we investigate inscribability of order types. We first show that every simple order type with at most 2 interior points is inscribable, and that the number of such order …

Given a hypergraph $H=(V,E)$, we say that $H$ is (weakly) $m$-colorable if there is a coloring $c:V\to$ such that every hyperedge of $H$ is not monochromatic. The (weak) chromatic number of $H$, denoted by $\chi (H)$, is the smallest $m$ such that $H$ is $m$-colorable. A vertex subset $T\subseteq V$ is called a transversal …