摘要
Let G be a graph that can be embedded in a surface sigma of Euler characteristic c '(sigma). In this paper, we proved that there exists an integer increment 0 = 4 center dot (5 +root 49 - 24c ') center dot [2 - c ' + 21(5 +root 49 - 24c ')] such that the total chromatic number of G is increment (G) + 1 if increment (G) >= increment 0.
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