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On the Total Coloring of Graphs Embeddable in Surfaces

Authors:	Zhao Yue

Institution:	Department of Mathematics and Computer Science, Benedict College Columbia, SC 29204-1086, USA zhao{at}math.ohio-state.edu

Abstract:	The paper shows that any graph G with the maximum degree ${Delta}$ (G) $≥$ 8, which is embeddable in a surface ${Sigma}$ of Euler characteristic ${chi}$ ( ${Sigma}$ ) $≥$ 0, is totally ( ${Delta}$ (G)+2)-colorable. In general, it is shownthat any graph G which is embeddable in a surface ${Sigma}$ and satisfiesthe maximum degree ${Delta}$ (G) $≥$ (20/9) (3– ${chi}$ ( ${Sigma}$ ))+1 is totally ( ${Delta}$ (G)+2)-colorable.

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