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n-Tuple Coloring of Planar Graphs with Large Odd Girth

โœ Scribed by William Klostermeyer; Cun Quan Zhang


Publisher
Springer Japan
Year
2002
Tongue
English
Weight
149 KB
Volume
18
Category
Article
ISSN
0911-0119

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โœ Klostermeyer, William; Zhang, Cun Quan ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 258 KB ๐Ÿ‘ 3 views

The odd-girth of a graph is the length of a shortest odd circuit. A conjecture by Pavol Hell about circular coloring is solved in this article by showing that there is a function f ( ) for each : 0 < < 1 such that, if the odd-girth of a planar graph G is at least f ( ), then G is (2 + )-colorable. N

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It is proved that if G is a planar graph with total (vertex-edge) chromatic number ฯ‡ , maximum degree and girth g, then ฯ‡ = + 1 if โ‰ฅ 5 and g โ‰ฅ 5, or โ‰ฅ 4 and g โ‰ฅ 6, or โ‰ฅ 3 and g โ‰ฅ 10. These results hold also for graphs in the projective plane, torus and Klein bottle.

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