2-distance list (Δ+ 3)-coloring of sparse graphs

05/04/2021

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by   Hoang La, et al.

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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 (Δ + 3)-coloring for graphs with maximum average degree less than 8/3 and maximum degree Δ≥ 4 as well as graphs with maximum average degree less than 14/5 and maximum degree Δ≥ 6.