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A vertex coloring of a graph G is called a 2-distance coloring if any two vertices at a distance at most 2 from each other receive different colors. Recently, Bousquet et al. (Discrete Mathematics, 346 (4), 113288, 2023) proved that 2+7 colors are sufficient for the 2-distance coloring of planar graphs with maximum degree 9. In this paper, we strengthen their result by removing the maximum degree constraint and show that all planar graphs admit a 2-distance (2+7) -coloring. This particularly improves the result of Van den Heuvel and McGuinness (Journal of Graph Theory, 42 (2), 110-124, 2003).
Zakir Deniz (2024) studied this question.