2-distance list $(\Delta +3)$-coloring of sparse graphs

Abstract

A 2-distance list k-coloring of a graph is a proper coloring of the vertices where each vertex has a list of at least k available colors and vertices at distance at most 2 cannot share the same color. We prove the existence of a 2-distance list $(\Delta +3)$-coloring for graphs with maximum average degree less than $\frac{8}{3}$ and maximum degree $\Delta \ge 4$ as well as graphs with maximum average degree less than $\frac{14}{5}$ and maximum degree $\Delta \ge 6$.

7 pages. arXiv admin note: text overlap with arXiv:2103.11687

References in corpus (1)

• The chromatic number of the square of subcubic planar graphs