Abstract
A 2-distance coloring of a graph is a coloring of the vertices such that two vertices at distance at most two receive distinct colors. A list assignment of a graph G is a mapping L which assigns to each vertex v a set L(v) of positive integers. The list 2-distance chromatic number of G denoted by \(\chi_2^l\left(G \right)\) is the least integer k for which G is list 2-distance k-colorable. In this paper, we prove that every planar graph with g(G) ≥ 5 and Δ(G) ≥ 40 is list 2-distance (Δ(G) + 4)-colorable.
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The authors thank the editors and anonymous referees for their valuable comments and suggestions.
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This paper is supported by the National Natural Science Foundation of China (Nos. 11771443, 12071265).
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Jin, Yd., Miao, Ly. List 2-distance Coloring of Planar Graphs with Girth Five. Acta Math. Appl. Sin. Engl. Ser. 38, 540–548 (2022). https://doi.org/10.1007/s10255-022-1097-1
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DOI: https://doi.org/10.1007/s10255-022-1097-1