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An upper bound for the total chromatic number of dense graphs. (English) Zbl 0767.05048
Let $$\chi''(G)$$ be the total chromatic number, $$\Delta(G)$$ be the maximum degree, and $$n$$ the order of a graph $$G$$. This paper shows that $$\chi''(G)\leq\Delta(G)+2k+1$$ when $$\Delta(G)\geq n/k$$, where $$k$$ is a (small) positive integer.

##### MSC:
 05C15 Coloring of graphs and hypergraphs
##### Keywords:
upper bound; dense graphs; total chromatic number
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##### References:
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