The List 2-Distance Coloring of Sparse Graphs

Abstract

The k-2-distance coloring of a graph G is a mapping (Formula Presented) such that for every pair of (Formula Presented) satisfying (Formula Presented). A graph G is list 2-distance k-colorable if any list L of admissible colors on V(G) of size k allows a 2-distance coloring (Formula Presented) such that (Formula Presented). The least k for which G is list 2-distance k-colorable is denoted by (Formula Presented). In this paper, we proved that if a graph G with the maximum average degree (Formula Presented) and (Formula Presented), then (Formula Presented); if a graph G with (Formula Presented).