24 citations · 69 across the 8 of their papers we have counts for
12 papers
Uniformly Random Colourings of Sparse Graphs
Eoin Hurley, François Pirot
We analyse uniformly random proper -colourings of sparse graphs with maximum degree in the regime . This regime corresponds to the lower side of the shattering t…
Asymptotic Dimension of Minor-Closed Families and Assouad-Nagata Dimension of Surfaces
Marthe Bonamy, Nicolas Bousquet, Louis Esperet +4
The asymptotic dimension is an invariant of metric spaces introduced by Gromov in the context of geometric group theory. In this paper, we study the asymptotic dimension of metric…
Packing and covering balls in graphs excluding a minor
Nicolas Bousquet, Wouter Cames van Batenburg, Louis Esperet +4
We prove that for every integer there exists a constant such that for every -minor-free graph , and every set of balls in , the minimum size of a set…
Variations on the Petersen colouring conjecture
François Pirot, Jean-Sébastien Sereni, Riste Škrekovski
The Petersen colouring conjecture states that every bridgeless cubic graph admits an edge-colouring with colours such that for every edge , the set of colours assigned to th…
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…
Fractional chromatic number, maximum degree and girth
François Pirot, Jean-Sébastien Sereni
We introduce a new method for computing bounds on the independence number and fractional chromatic number of classes of graphs with local constraints, and apply this method in vari…
Strong cliques and forbidden cycles
Wouter Cames van Batenburg, Ross J. Kang, François Pirot
Given a graph , the strong clique number of is the cardinality of a largest collection of edges every pair of which are incident or connected by an edge in . We…
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…
Colouring triangle-free graphs with local list sizes
Ewan Davies, Rémi de Joannis de Verclos, Ross J. Kang +1
We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow-up work of Bernshteyn) on the (list) chromatic number of triangle-free graphs.…
Bipartite induced density in triangle-free graphs
Wouter Cames van Batenburg, Rémi de Joannis de Verclos, Ross J. Kang +1
We prove that any triangle-free graph on vertices with minimum degree at least contains a bipartite induced subgraph of minimum degree at least . This is sharp up…
Distance colouring without one cycle length
Ross J. Kang, François Pirot
We consider distance colourings in graphs of maximum degree at most and how excluding one fixed cycle length affects the number of colours required as . For…
Colouring powers and girth
Ross J. Kang, François Pirot
Alon and Mohar (2002) posed the following problem: among all graphs of maximum degree at most and girth at least , what is the largest possible value of , the ch…