n-Tuple Coloring of Planar Graphs with Large Odd Girth

نویسندگان

William Klostermeyer

Cun-Quan Zhang

چکیده

The main result of the papzer is that any planar graph with odd girth at least 10k À 7 has a homomorphism to the Kneser graph G 2k1 k , i.e. each vertex can be colored with k colors from the set f1; 2;. .. ; 2k 1g so that adjacent vertices have no colors in common. Thus, for example, if the odd girth of a planar graph is at least 13, then the graph has a homomorphism to G 5 2 , also known as the Petersen graph. Other similar results for planar graphs are also obtained with better bounds and additional restrictions.

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