15 citations · 28 across the 7 of their papers we have counts for
8 papers
A Domatic Analogue of -Bounded Graph Classes and the Gyárfás-Sumner Conjecture
Quentin Chuet, Selma Djelloul, Hoang La +2
Given a graph , a dominating set is a subset such that . The \emph{domatic number} of , denoted , is the maximum size of a partitio…
Chromatic discrepancy of locally -colourable graphs
Timothée Corsini, Lucas Picasarri-Arrieta, Théo Pierron +2
The chromatic discrepancy of a graph , denoted , is the least over all proper colourings of of the greatest difference between the number of colours sp…
Minimum acyclic number and maximum dichromatic number of oriented triangle-free graphs of a given order
Pierre Aboulker, Frédéric Havet, François Pirot +1
Let be a digraph. Its acyclic number is the maximum order of an acyclic induced subdigraph and its dichromatic number is the least integer such that $…
Colouring locally sparse graphs with the first moment method
François Pirot, Eoin Hurley
We give a short proof of a bound on the list chromatic number of graphs of maximum degree where each neighbourhood has density at most , namely $χ_\ell(G) \le (1+o(1)) \…
Distributed algorithms for fractional coloring
Nicolas Bousquet, Louis Esperet, François Pirot
In this paper we study fractional coloring from the angle of distributed computing. Fractional coloring is the linear relaxation of the classical notion of coloring, and has many a…
Surfaces have (asymptotic) dimension 2
Marthe Bonamy, Nicolas Bousquet, Louis Esperet +3
The asymptotic dimension is an invariant of metric spaces introduced by Gromov in the context of geometric group theory. When restricted to graphs and their shortest paths metric,…
An algorithmic framework for colouring locally sparse graphs
Ewan Davies, Ross J. Kang, François Pirot +1
We develop an algorithmic framework for graph colouring that reduces the problem to verifying a local probabilistic property of the independent sets. With this we give, for any fix…
Graph structure via local occupancy
Ewan Davies, Ross J. Kang, François Pirot +1
The first author together with Jenssen, Perkins and Roberts (2017) recently showed how local properties of the hard-core model on triangle-free graphs guarantee the existence of la…