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Total colorings of graphs of order $$2n$$ having maximum degree $$2n-2$$. (English) Zbl 0771.05034
Summary: Let $$\chi_ t(G)$$ and $$\Delta(G)$$ denote respectively the total chromatic number and maximum degree of graph $$G$$. H. P. Yap, J.-F. Wang and Z. Zhang [J. Aust. Math. Soc., Ser. A 47, No. 3, 445-452 (1989; Zbl 0702.05032)] proved that if $$G$$ is a graph of order $$p$$ having $$\Delta(G)\geq p-4$$, then $$\chi_ t(G)\leq\Delta(G)+2$$. Hilton has characterized the class of graphs $$G$$ of order $$2n$$ having $$\Delta(G)=2n-1$$ such that $$\chi_ t(G)=\Delta(G)+2$$. In this paper, we characterize the class of graphs $$G$$ of order $$2n$$ having $$\Delta(G)=2n- 2$$ such that $$\chi_ t(G)=\Delta(G)+2$$.

##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C75 Structural characterization of families of graphs
##### Keywords:
total colorings; chromatic number; maximum degree
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##### References:
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