We prove that for all 0 ≤ t ≤ k and d ≥ 2k, every graph G with treewidth at most k has a ‘large’ induced subgraph H, where H has treewidth at most t and every vertex in ...
The slope-number of a graph G is the minimum number of distinct edge slopes in a straight-line drawing of G in the plane. We prove that for Δ 5 and all large n, there is a Δ-reg...
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has bee...
A vertex v of a graph G is a boundary vertex if there exists a vertex u such that the distance in G from u to v is at least the distance from u to any neighbour of v. We give the ...
For graphs of bounded maximum degree, we consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges between two colour cl...
Louigi Addario-Berry, Louis Esperet, Ross J. Kang,...