A note on acyclic total coloring of plane graphs

作者：Dong, Wei^*

来源：Ars Combinatoria, 2016, 129: 123-137.

• total coloring
• plane graph
• acyclic coloring
• acyclic total coloring

An acyclic total coloring is a proper total coloring of a graph G such that there are at least 4 colors on vertices and edges incident with a cycle of G. The acyclic total chromatic number of G, chi(a)''(G), is the least number of colors in an acyclic total coloring of G. In this paper, we prove that for every plane graph G with maximum degree Delta and girth g(G), chi(a)''(G) = Delta + 1 if (1) Delta >= 9 and g(G) >= 4; (2) Delta >= 6 and g(G) >= 5; (3) Delta >= 4 and g(G) >= 6; (4) Delta >= 3 and g(G) >= 14.

• 出版日期2016-10
• 单位南京晓庄学院