| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 419424 | Discrete Applied Mathematics | 2012 | 7 Pages |
Abstract
A total kk-coloring of a graph GG is a coloring of V(G)∪E(G)V(G)∪E(G) using kk colors such that no two adjacent or incident elements receive the same color. The total chromatic number of GG is the smallest integer kk such that GG has a total kk-coloring. In this paper, it is proved that if GG is a planar graph with maximum degree Δ≥7Δ≥7 and without intersecting 55-cycles, that is, every vertex is incident with at most one cycle of length 55, then the total chromatic number of GG is Δ+1Δ+1.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Bing Wang, Jian-Liang Wu,