On-Hei Solomon Lo, Minors of non-hamiltonian graphs
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 …
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, …
The 2025 Summer School on Combinatorics and Algorithms is a venue for students and early-career researchers to learn selected topics in theoretical computer science and discrete mathematics. It will be …
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 …