2-Distance coloring of planar graphs without short cycles

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The k-2-distance coloring of a graph G is a mapping c: V (G) →{ 1, 2, ··· ,k } such that for every pair of u, v satisfying 0 <d G(u, v) ≤ 2, c(u) � c(v). The minimum number of colors in 2-distance coloring of G is its 2-distance chromatic number, denoted by χ2(G). In this paper, we prove that every planar graph without 3, 4, 8-cycles and Δ ≥ 14 is (Δ + 5)-2-distance colorable.