List 3-dynamic coloring of graphs with small maximum average degree

Abstract

An r-dynamic k-coloring of a graph G is a proper k-coloring such that for any vertex v, there are at least min{r, deg G (v)} distinct colors in N G (v). The r-dynamic chromatic number χ d r (G) of a graph G is the least k such that there exists an r-dynamic k-coloring of G. The list r-dynamic chromatic number of a graph G is denoted by ch

On list 3-dynamic coloring of near-triangulations

“…Several results about r-dynamic coloring were published in [1,2,5,6,7,11]. In term of maximum average degree, there is a result published in [8]. And some special classes of graphs are also investigated, such as K 4 -minor free graphs [13], K 1,3 -free graphs [10] and bipartite graphs [3].…”