New bounds for odd colourings of graphs

Tianjiao Dai, Qiancheng Ouyang, François Pirot

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