6 papers · 1 filter
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…
Frugal colourings of graphs via sparse hypergraph colouring
Quentin Chuet
A proper colouring of a graph is -frugal if every colour appears at most times in the neighbourhood of each vertex. Let denote the minimum number of colours nee…
Inversion diameter and 2-edge-colored homomorphisms
Carmen Arana, Thomas Bellitto, Hector Buffière +3
In an oriented graph, the inversion of a subset of vertices X is the operation reversing the direction of every arc with both endpoints in X. Given a graph G, the inversion distanc…
Fractional domatic number and minimum degree
Quentin Chuet, Hugo Demaret, Hoang La +1
The domatic number of a graph is the maximum number of pairwise disjoint dominating sets of . We are interested in the LP-relaxation of this parameter, which is called the f…
New bounds for proper -conflict-free colourings
Quentin Chuet, Tianjiao Dai, Qiancheng Ouyang +1
A proper -colouring of a graph is called -conflict-free if every vertex has at least colours appearing exactly once in its neighbourhood.…
A note on locating-dominating sets in twin-free graphs
Nicolas Bousquet, Quentin Chuet, Victor Falgas-Ravry +2
In this short note, we prove that every twin-free graph on vertices contains a locating-dominating set of size at most . This improves the earlier bou…