A 2-distance $(2Δ+7)$-coloring of planar graphs

Paper

Abstract

A vertex coloring of a graph

is called a

-distance coloring if any two vertices at a distance at most

from each other receive different colors. Recently, Bousquet et al. (Discrete Mathematics, 346(4), 113288, 2023) proved that

colors are sufficient for the

-distance coloring of planar graphs with maximum degree

. In this paper, we strengthen their result by removing the maximum degree constraint and show that all planar graphs admit a 2-distance

-coloring. This particularly improves the result of Van den Heuvel and McGuinness (Journal of Graph Theory, 42(2), 110-124, 2003).