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Total colorings of planar graphs with maximum degree at least 8

โœ Scribed by Lan Shen; YingQian Wang


Publisher
SP Science China Press
Year
2009
Tongue
English
Weight
319 KB
Volume
52
Category
Article
ISSN
1674-7283

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Total colorings of planar graphs with la
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It is proved that a planar graph with maximum degree โˆ† โ‰ฅ 11 has total (vertex-edge) chromatic number โˆ† + 1.

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Given a graph G, a total k-coloring of G is a simultaneous coloring of the vertices and edges of G with at most k colors. If โˆ†(G) is the maximum degree of G, then no graph has a total โˆ†-coloring, but Vizing conjectured that every graph has a total (โˆ† + 2)-coloring. This Total Coloring Conjecture rem

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## Abstract In this article we prove that the total chromatic number of a planar graph with maximum degree 10 is 11. ยฉ 2006 Wiley Periodicals, Inc. J Graph Theory 54: 91โ€“102, 2007