List 3-dynamic coloring of graphs with small maximum average degree |
| |
Authors: | Seog-Jin Kim Boram Park |
| |
Affiliation: | 1. Department of Mathematics Education, Konkuk University, Seoul, Republic of Korea;2. Department of Mathematics, Ajou University, Suwon, Republic of Korea |
| |
Abstract: | An -dynamic -coloring of a graph is a proper -coloring such that for any vertex , there are at least distinct colors in . The -dynamic chromatic number of a graph is the least such that there exists an -dynamic -coloring of . The list-dynamic chromatic number of a graph is denoted by .Recently, Loeb et al. (0000) showed that the list -dynamic chromatic number of a planar graph is at most 10. And Cheng et al. (0000) studied the maximum average condition to have , or . On the other hand, Song et al. (2016) showed that if is planar with girth at least 6, then for any .In this paper, we study list 3-dynamic coloring in terms of maximum average degree. We show that if , if , and if . All of the bounds are tight. |
| |
Keywords: | Dynamic coloring List 3-dynamic coloring Maximum average degree |
本文献已被 ScienceDirect 等数据库收录! |
|