François Pirot

most citedNew bounds for odd colourings of graphs

1 citations · 2 across the 2 of their papers we have counts for

collaborators

2 papers

math.CO2023★ 1 cited

New bounds for odd colourings of graphs

Tianjiao Dai, Qiancheng Ouyang, François Pirot

Given a graph $G$ , a vertex-colouring $σ$ of $G$ , and a subset $X \subseteq V (G)$ , a colour $x \in σ (X)$ is said to be \emph{odd} for $X$ in $σ$ if it has an odd number of occurrenc…

math.CO2023★ 1 cited

Uniformly Random Colourings of Sparse Graphs

Eoin Hurley, François Pirot

We analyse uniformly random proper $k$ -colourings of sparse graphs with maximum degree $Δ$ in the regime $Δ < k ln k$ . This regime corresponds to the lower side of the shattering t…