LIST INJECTIVE COLORING OF PLANAR GRAPHS WITH GIRTH AT LEAST FIVE

. 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(l)(i) (G). For a planar graph G, Bu et al. proved that chi(l)(i)(G) < Delta + 6 if girth g >= 5 and maximum degree Delta(G) >= 8. In this paper, we improve this result by showing that chi li(G) < Delta + 6 for g >= 5 and arbitrary Delta(G).