Acyclic total colorings of planar graphs without l cycles

作者：Sun, Xiang Yong^*; Wu, Jian Liang

来源：Acta Mathematica Sinica-English Series, 2011, 27(7): 1315-1322.

DOI：10.1007/s10114-011-8640-y

• Acyclic total coloring
• cycle
• planar graph

A proper total coloring of a graph G such that there are at least 4 colors on those vertices and edges incident with a cycle of G, is called acyclic total coloring. The acyclic total chromatic number of G is the least number of colors in an acyclic total coloring of G. In this paper, it is proved that the acyclic total chromatic number of a planar graph G of maximum degree at least k and without l cycles is at most Delta(G) + 2 if (k, l) a {(6, 3), (7, 4), (6, 5), (7, 6)}.

• 出版日期2011-7
• 单位山东财经大学; 山东大学