A Unified Approach to Distance-Two Colouring of Graphs on Surfaces

Omid Amini, Louis Esperet, Jan van den Heuvel

In this paper we introduce the notion of $\Sigma$-colouring of a graph $G$: For given subsets $\Sigma (v)$ of neighbours of $v$, for every $v\in V(G)$, this is a proper colouring of the verti…