2-distance (Δ+2)-coloring of sparse graphs

09/24/2021

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by   Hoang La, et al.

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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 (Δ+2)-coloring for graphs with maximum average degree less than 8/3 (resp. 14/5) and maximum degree Δ≥ 6 (resp. Δ≥ 10). As a corollary, every planar graph with girth at least 8 (resp. 7) and maximum degree Δ≥ 6 (resp. Δ≥ 10) admits a 2-distance (Δ+2)-coloring.