List injective coloring of planar graphs with girth g ≥ 6

A vertex coloring of a graph G is called injective if any two vertices with a common neighbor receive distinct colors. A graph G is injectively k-choosable if any list L of admissible colors on V(G) of size k allows an injective coloring phi such that phi(v) is an element of L(v) whenever v is an element of V(G). The least k for which G is injectively k-choosable is denoted by chi(1)(i)(G). In this paper, we show that if G is a planar graph with girth g >= 6, then chi(1)(i)(G) <= Delta + 3. (C) 2016 Elsevier B.V. All rights reserved.