We show that planar graphs have bounded queue-number, thus proving a conjecture of
Heath et al.[66] from 1992. The key to the proof is a new structural tool called layered …

We show that there exists an adjacency labelling scheme for planar graphs where each
vertex of an n-vertex planar graph G is assigned a (1+ o (1)) log 2 n-bit label and the labels …

It was recently proved that every planar graph is a subgraph of the strongproduct of a path
and a graph with bounded treewidth. This paper surveys generalisationsof this result for …

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 …

Graph product structure theory expresses certain graphs as subgraphs of the strong product
of much simpler graphs. In particular, an elegant formulation for the corresponding structural …

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 …

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 …

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

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 …

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 …