Seokbeom Kim (김석범), The structure of △(1, 2, 2)-free tournaments
Room B332 IBS (기초과학연구원)Given a tournament
Given a tournament
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
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
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 …
The matroid intersection problem is a fundamental problem in combinatorial optimization. In this problem we are given two matroids and the goal is to find the largest common independent set …