기초과학연구원 이산수학그룹
Ramsey's theorem states that, for a fixed graph $H$, every 2-edge-colouring of $K_n$ contains a monochromatic copy of $H$ whenever $n$ is large enough. Perhaps one of the most natural …
There has been much research on finding a large rainbow matching in a properly edge-colored graph, where a proper edge coloring is a coloring of the edge set such that …
A graph $H$ is common if the number of monochromatic copies of $H$ in a 2-edge-colouring of the complete graph $K_n$ is minimised by the random colouring. Burr and Rosta, extending …
I will go over the history on the study of the set of cycle lengths of graphs with large average degree or chromatic number, and discuss recent work with Richard …
Given a graph G=(V,E), the independence complex of G is the abstract simplicial complex I(G) on V whose faces are the independent sets of G. A graph is ternary if it does …
The canonical tree-decomposition theorem, proved by Robertson and Seymour in their seminal graph minors series, turns out to be an extremely valuable tool in structural and algorithmic graph theory. In …
The notion of convexity spaces provides a purely combinatorial framework for certain problems in discrete geometry. In the last ten years, we have seen some progress on several open problems …
We show that each perfect matching in a bipartite graph G intersects at least half of the perfect matchings in G. This result has equivalent formulations in terms of the permanent …
A family $\mathcal F$ of subsets of is called s-saturated if it contains no s pairwise disjoint sets, and moreover, no set can be added to $\mathcal F$ while preserving …
Main purpose of this talk is to introduce a connection between restriction estimates for cones and point-sphere incidence theorems in the finite field setting. First, we review the finite field …