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An Oriented 6-Coloring of Planar Graphs with Girth at Least 9

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Abstract

We prove that every oriented graph with a maximum average degree less than 18/7 admits a homomorphism into \(P_{7}^{*}\), the Paley tournament of order seven with one vertex deleted. In particular, every oriented planar graph of girth at least 9 has a homomorphism into \(P_{7}^{*}\), whence every planar graph of girth at least 9 has oriented chromatic number at most 6.

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  1. American University of Sharjah, P.O. Box 26666, Sharjah, UAE

    T. H. Marshall

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  1. T. H. Marshall
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Correspondence to T. H. Marshall.

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Marshall, T.H. An Oriented 6-Coloring of Planar Graphs with Girth at Least 9. Graphs and Combinatorics 32, 1101–1116 (2016). https://doi.org/10.1007/s00373-015-1612-8

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  • DOI: https://doi.org/10.1007/s00373-015-1612-8

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