기초과학연구원 이산수학그룹
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, …
We formulate a geometric version of the Erdős-Hajnal conjecture that applies to finite projective geometries rather than graphs. In fact, we give a natural extension of the 'multicoloured' version of …
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 …
We prove that for any circle graph $H$ with at least one edge and for any positive integer $k$, there exists an integer $t=t(k,H)$ so that every graph $G$ either …
Lehel's conjecture states that every 2-edge-colouring of the complete graph $K_n$ admits a partition of its vertices into two monochromatic cycles. This was proven for sufficiently large n by Luczak, …
We will discuss two symmetry breaking parameters: distinguishing number and fixing number. Despite being introduced independently, they share meaningful connections. In particular, we show that if a tree is 2-distinguishable …
We prove that for all positive integers $k$ and $d$, the class of $K_{1,d}$-free graphs not containing the $k$-ladder or the $k$-wheel as an induced minor has a bounded tree-independence …