Abstract
We give a new upper bound on the total chromatic number of a graph. This bound improves the results known for some classes of graphs. The bound is stated as follows: χ T ⩽ χ e + ⌊ 1 3 χ⌋ + 2 , where χ is the chromatic number, χ e is the edge chromatic number (chromatic index) and χ T is the total chromatic number.
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