List 2-distance Coloring of Planar Graphs with Girth Five

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(l)(2)(G) 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 Delta(G) >= 40 is list 2-distance (Delta(G) + 4)-colorable.