List 2-distance coloring of planar graphs without short cycles
Yuehua Bu, Chunhui Shang · Discrete Mathematics Algorithms and Applications · 2015
A 2-distance coloring of [Formula: see text] is a function [Formula: see text]: [Formula: see text], such that for every two distinct vertices [Formula: see text], [Formula: see text] in [Formula: see text], [Formula: see text] if [Formula: see text]. The 2-distance chromatic number of [Formula: see text] is the least integer [Formula: see text] such that [Formula: see text] has a [Formula: see text]-[Formula: see text]-distance coloring, denoted by [Formula: see text]. Similarly, the list 2-distance chromatic number of [Formula: see text] is denoted by [Formula: see text]. In this paper, we proved that: (1) for every planar graph with [Formula: see text] and [Formula: see text], [Formula: see text]; (2) for every planar graph with [Formula: see text] and [Formula: see text], [Formula: see text].