| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4648295 | Discrete Mathematics | 2011 | 6 Pages |
Abstract
Let GG be a planar graph with maximum degree Δ≥7Δ≥7 and without intersecting 3-cycles; that is, two cycles of length 3 are not incident with a common vertex. Then the total chromatic number of GG is Δ+1Δ+1.
► In this study, we investigate total colorings of planar graphs with maximum degree seven. ► We use the discharging method in the proofs. ► It is proved that, if a planar graph GG contains no intersecting triangles and Δ(G)≥7Δ(G)≥7, then χ″(G)=Δ+1χ″(G)=Δ+1.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Bing Wang, Jian-Liang Wu,