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ON THE TOTAL COLORING OF GRAPHS EMBEDDABLE IN SURFACES

Published online by Cambridge University Press:  01 October 1999

YUE ZHAO
YUE ZHAO
Affiliation:
Department of Mathematics and Computer Science, Benedict College, Columbia, SC 29204-1086, USA; [email protected] Current address: Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364, USA.
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Abstract

The paper shows that any graph G with the maximum degree Δ(G) [ges ] 8, which is embeddable in a surface Σ of Euler characteristic χ(Σ) [ges ] 0, is totally (Δ(G)+2)-colorable. In general, it is shown that any graph G which is embeddable in a surface Σ and satisfies the maximum degree Δ(G) [ges ] (20/9) (3−χ(Σ))+1 is totally (Δ(G)+2)-colorable.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 2 , October 1999 , pp. 333 - 343
Copyright
The London Mathematical Society 1999

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