n-Tuple Coloring of Planar Graphs with Large Odd Girth

 The main result of the papzer is that any planar graph with odd girth at least 10k−7 has a homomorphism to the Kneser graph G _k ^{2 k +1}, i.e. each vertex can be colored with k colors from the set {1,2,…,2k+1} 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 ₂ ⁵, also known as the Petersen graph. Other similar results for planar graphs are also obtained with better bounds and additional restrictions.

Authors and Affiliations

1. Department of Computer and Information Sciences, University of North Florida, Jacksonville, FL 32224, USA. e-mail: klostermeyer@hotmail.com, , , , , , US

   William Klostermeyer

2. Department of Mathematics, P. O. Box 6310, West Virginia University, Morgantown, WV 26506, USA. e-mail: cqzhang@math.wvu.edu, , , , , , US

   Cun Quan Zhang

Received: June 14, 1999 Final version received: July 5, 2000

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