F. Pirot

collaborators

5 papers

math.CO2019

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 $5$ colours such that for every edge $e$ , the set of colours assigned to th…

math.CO2019

Strong cliques and forbidden cycles

Wouter Cames van Batenburg, Ross J. Kang, François Pirot

Given a graph $G$ , the strong clique number $ω_{2}^{'} (G)$ of $G$ is the cardinality of a largest collection of edges every pair of which are incident or connected by an edge in $G$ . We…

math.CO2018

Occupancy fraction, fractional colouring, and triangle fraction

Ewan Davies, Rémi de Joannis de Verclos, Ross J. Kang +1

Given $ε > 0$ , there exists $f_{0}$ such that, if $f_{0} \leq f \leq Δ^{2} + 1$ , then for any graph $G$ on $n$ vertices of maximum degree $Δ$ in which the neighbourhood of every vert…

math.CO2018

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.…

math.CO2018

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 $n$ vertices with minimum degree at least $d$ contains a bipartite induced subgraph of minimum degree at least $d^{2} / (2 n)$ . This is sharp up…