Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every
planar graph $ G $ there is a graph $ H $ with treewidth at most 8 and a path $ P $ such that …

Hadwiger's Conjecture asserts that every K_h-minor-free graph is properly (h-1)-colourable.
We prove the following improper analogue of Hadwiger's Conjecture: for fixed h, every K_h …

The planar graph product structure theorem of Dujmović et al.[J. ACM, 67 (2020), 22] states
that every planar graph is a subgraph of the strong product of a graph with bounded …

We prove that for every planar graph X of treedepth h, there exists a positive integer c such
that for every X-minor-free graph G, there exists a graph H of treewidth at most f (h) such that …

Stanislaw Ulam asked whether there exists a universal countable planar graph (that is, a
countable planar graph that contains every countable planar graph as a subgraph). J\'anos …

An adjacency labeling scheme for a given class of graphs is an algorithm that for every
graph G from the class, assigns bit strings (labels) to vertices of G so that for any two vertices …

Product structure of graph classes with bounded treewidth Page 1 Combinatorics, Probability
and Computing (2023), 1–26 doi:10.1017/S0963548323000457 ARTICLE Product structure of …

Clustered 3-colouring graphs of bounded degree Page 1 Combinatorics, Probability and
Computing (2022), 31, pp. 123–135 doi:10.1017/S0963548321000213 ARTICLE Clustered …

Dujmovic, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every
graph G with Euler genus g there is a graph H with treewidth at most 4 and a path P such …

This paper shows that $ K_t $-minor-free (and $ K_ {s, t} $-minor-free) graphs $ G $ are
subgraphs of products of a tree-like graph $ H $(of bounded treewidth) and a complete …