2-Distance List $$(\varDelta +3)$$-Coloring of Sparse Graphs

Abstract

A 2-distance k-coloring of a graph is a proper k-coloring of the vertices where vertices at distance at most 2 cannot share the same color. We prove the existence of a 2-distance (∆ + 2)-coloring for graphs with maximum average degree less than 8 3 (resp. 14 5 ) and maximum degree ∆ ≥ 6 (resp. ∆ ≥ 10). As a corollary, every planar graph with girth at least 8 (resp. 7) and maximum degree ∆ ≥ 6 (resp. ∆ ≥ 10) admits a 2-distance (∆ + 2)-coloring.