24 citations · 26 across the 7 of their papers we have counts for
11 papers
Chordal directed graphs are not -bounded
Pierre Aboulker, Nicolas Bousquet, Rémi de Verclos
We show that digraphs with no transitive tournament on vertices and in which every induced directed cycle has length can have arbitrarily large dichromatic number. This ans…
Maximising line subgraphs of diameter at most
Stijn Cambie, Wouter Cames van Batenburg, Rémi de Joannis de Verclos +1
We wish to bring attention to a natural but slightly hidden problem, posed by Erdős and Nešetřil in the late 1980s, an edge version of the degree--diameter problem. Our main result…
Structure and colour in triangle-free graphs
N. R. Aravind, Stijn Cambie, Wouter Cames van Batenburg +3
Motivated by a recent conjecture of the first author, we prove that every properly coloured triangle-free graph of chromatic number contains a rainbow independent set of size $…
Strong chromatic index and Hadwiger number
Wouter Cames van Batenburg, Rémi de Joannis de Verclos, Ross J. Kang +1
We investigate the effect of a fixed forbidden clique minor upon the strong chromatic index, both in multigraphs and in simple graphs. We conjecture for each that any $K_k…
Chordal graphs are easily testable
Rémi de Joannis de Verclos
We prove that the class of chordal graphs is easily testable in the following sense. There exists a constant such that, if adding/removing at most edges to a graph …
Occupancy fraction, fractional colouring, and triangle fraction
Ewan Davies, Rémi de Joannis de Verclos, Ross J. Kang +1
Given , there exists such that, if , then for any graph on vertices of maximum degree in which the neighbourhood of every vert…