摘要
A k-coloring of a graph G is a mapping c:V(G)→{1,2,···,k}.The coloring c is called injective if any two vertices have a common neighbor get distinct colors.A graph G is injectively k-choosable if for any color list L of admissible colors on V(G)of size k allows an injective coloringφsuch thatφ(v)∈L(v)for each v∈V(G).Letχ;(G),χ;(G)denote the injective chromatic number and injective choosability number of G,respectively.In this paper,we show thatχ;(G)≤△+4 if△≥22 andχ;(G)≤△+5 if△≥15,where G is a triangle-free planar graph and without intersecting 4-cycles.
基金
supported by the National Natural Science Foundation of China(Nos.12071351,11571258)。
