기초과학연구원 이산수학그룹
Branchwidth determines how graphs, and more generally, arbitrary connectivity (basically symmetric and submodular) functions could be decomposed into a tree-like structure by specific cuts. We develop a general framework for …
What is the largest number $f(d)$ where every graph with average degree at least $d$ contains a subdivision of $K_{f(d)}$? Mader asked this question in 1967 and $f(d) = \Theta(\sqrt{d})$ …
The independent domination number of a graph $G$, denoted $i(G)$, is the minimum size of an independent dominating set of $G$. In this talk, we prove a series of results regarding …
I will discuss various results for rainbow matching problems. In particular, I will introduce a ‘sampling trick’ which can be used to obtain short proofs of old results as well …
We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) well-spread, …
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 …
A geometric transversal to a family of convex sets in $\mathbb R^d$ is an affine flat that intersects the members of the family. While there exists a far-reaching theory concerning …
The Caccetta-Haggkvist conjecture, one of the best known in graph theory, is that in a digraph with $n$ vertices in which all outdegrees are at least $n/k$ there is a …
For given $k$ graphs $G_1,\dots, G_k$ over a common vertex set of size $n$, what conditions on $G_i$ ensures a 'colorful' copy of $H$, i.e. a copy of $H$ containing …
Graph Minor project by Robertson and Seymour is perhaps the deepest theory in Graph Theory. It gives a deep structural characterization of graphs without any graph $H$ as a minor. …