It is proved that a planar graph with maximum degree ∆ ≥ 11 has total (vertex-edge) chromatic number ∆ + 1.
Total colorings of graphs of order 2nhaving maximum degree 2n−2
✍ Scribed by Bor-Liang Chen; Hung-Lin Fu
- Publisher
- Springer Japan
- Year
- 1992
- Tongue
- English
- Weight
- 239 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0911-0119
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## Abstract Let ${\cal F}\_{{2}{k},{k}^{2}}$ consist of all simple graphs on 2__k__ vertices and ${k}^{2}$ edges. For a simple graph __G__ and a positive integer $\lambda$, let ${P}\_{G}(\lambda)$ denote the number of proper vertex colorings of __G__ in at most $\lambda$ colors, and let $f(2k, k^{2
Given a graph G, a total k-coloring of G is a simultaneous coloring of the vertices and edges of G with at most k colors. If ∆(G) is the maximum degree of G, then no graph has a total ∆-coloring, but Vizing conjectured that every graph has a total (∆ + 2)-coloring. This Total Coloring Conjecture rem