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

An r-dynamic k-coloring of a graph G is a proper k-coloring φ such that for any vertex v, v has at least min{r, degG(v)} distinct colors in NG(v). The r-dynamic chromatic number χr(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 chr(G). Recently, Loeb, Mahoney, Reiniger, and Wise showed that the list 3-dynamic chromatic number of a planar graph is at most 10. And Cheng, Lai, Lorenzen, Luo, Thompson, and Zhang studied the maximum average degree condition to have χ3(G) ≤ 4, 5, or 6. In this paper, we study list 3-dynamic coloring in terms of maximum average degree. We show that ch3(G) ≤ 6 if mad(G) < 18 7 , and ch d 3(G) ≤ 7 if mad(G) < 14 5 , and both of the bounds are tight. This is joint work with Boram Park.