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The total chromatic number of graphs of high minimum degree. (English) Zbl 0753.05033
Summary: If \(G\) is a simple graph with minimum degree \(\delta(G)\) satisfying \(\delta(G)\geq{5\over 6}(| V(G)|+1)\) the total chromatic number conjecture holds; moreover if \(\delta(G)\geq{3\over 4}| V(G)|\) then \(\chi_ T(G)\leq\Delta(G)+3\). Also if \(G\) has odd order and is regular with \(d(G)\geq{1\over 3}\sqrt 7| V(G)|\) then a necessary and sufficient condition for \(\chi_ T(G)=\Delta(G)+1\) is given.

MSC:
05C15 Coloring of graphs and hypergraphs
05C10 Planar graphs; geometric and topological aspects of graph theory
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