标题：Total coloring of planar graphs without 6-cycles
作者：Hou, J.;Liu, B.;Liu, G.;Wu, J.
作者机构：Center for Discrete Mathematics, Fuzhou University, Fuzhou 350002, China;School of Mathematics, Shandong University, Jinan 25010
来源：Discrete Applied Mathematics
关键词：Cycle;Planar graph;Total chromatic number;Total coloring
摘要：A totalk-coloring of a graph G is a coloring of V(G)∪E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ″(G) is the smallest integer k such that G has a total k-coloring. Let G be a planar graph with maximum degree Δ(G) and without 6-cycles. In this paper, it is proved that χ″(G)= Δ(G)+1 if Δ(G)<5 and G contains no 4-cycles, or Δ(G)<6 and G contains no 5-cycles.