by Michael Molloy, Bruce Reed, Equipe Combinatoire
Combinatorica
http://www.cs.toronto.edu/~molloy/webpapers/total.ps
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Abstract:
We prove that the total chromatic number of any graph with maximum degree \Delta is at most \Delta plus an absolute constant. In particular, we show that for \Delta sufficiently large, the total chromatic number of such a graph is at most \Delta + 10
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