기초과학연구원 이산수학그룹
Given a tournament $S$, a tournament is $S$-free if it has no subtournament isomorphic to $S$. Until now, there have been only a small number of tournaments $S$ such that …
Motivated by colouring minimal Cayley graphs, in 1978 Babai conjectured that no-lonely-colour graphs have bounded chromatic number. We disprove this in a strong sense by constructing graphs of arbitrarily large …
The now classical theorem of Erdős, Ko and Rado establishes the size of a maximal uniform family of pairwise-intersecting sets as well as a characterization of the families attaining such …
A seminal result of Tutte asserts that every 4-connected planar graph is hamiltonian. By Wagner's theorem, Tutte's result can be restated as: every 4-connected graph with no $K_{3,3}$ minor is …
Two celebrated extensions of Helly's theorem are the Fractional Helly theorem of Katchalski and Liu (1979) and the Quantitative Volume theorem of Barany, Katchalski, and Pach (1982). Improving on several …
Let $\mathcal F$ be a fixed, finite family of graphs. In the $\mathcal F$-Deletion problem, the input is a graph G and a positive integer k, and the goal is …
The notion of asymptotic dimension of metric spaces, introduced by Gromov, describes their large-scale behaviour. Asymptotic dimension of graph families has been recently studied, in particular, by Bonamy et al. …
We will discuss classical and recent results about phase transitions in random subgraphs of the hypercube and beyond. The focus will be on the giant component, long cycles, large matchings, …
A local certification of a graph property is a protocol in which nodes are given “certificates of a graph property” that allow the nodes to check whether their network has this …
This talk is an introduction to the recent notion of merge-width, proposed by Jan Dreier and Szymon Torúnczyk. I will give an overview of the context and motivations for merge-width, …