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n-Tuple Coloring of Planar Graphs with Large Odd Girth

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Abstract.

 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.

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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

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  1. William Klostermeyer
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  2. Cun Quan Zhang
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Received: June 14, 1999 Final version received: July 5, 2000

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Klostermeyer, W., Zhang, C. n-Tuple Coloring of Planar Graphs with Large Odd Girth. Graphs Comb 18, 119–132 (2002). https://doi.org/10.1007/s003730200007

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  • DOI: https://doi.org/10.1007/s003730200007

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