| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4649607 | Discrete Mathematics | 2009 | 9 Pages |
Abstract
Suppose that GG is a planar graph with maximum degree ΔΔ and without intersecting 4-cycles, that is, no two cycles of length 4 have a common vertex. Let χ″(G)χ″(G), χl′(G) and χl″(G) denote the total chromatic number, list edge chromatic number and list total chromatic number of GG, respectively. In this paper, it is proved that χ″(G)=Δ+1χ″(G)=Δ+1 if Δ≥7Δ≥7, and χl′(G)=Δ and χl″(G)=Δ+1 if Δ(G)≥8Δ(G)≥8. Furthermore, if GG is a graph embedded in a surface of nonnegative characteristic, then our results also hold.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Bin Liu, Jianfeng Hou, Jianliang Wu, Guizhen Liu,