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Facial Parity 9-Edge-Coloring of Outerplane Graphs

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Abstract

A facial parity edge-coloring of a \(2\)-edge-connected plane graph is such an edge-coloring in which no two face-adjacent edges receive the same color and in addition, for each face \(f\) and each color \(c\) either no edge or an odd number of edges incident with \(f\) is colored with \(c\). Let \(\chi _p^\prime (G)\) denote the minimum number of colors used in such a coloring of \(G\). In this paper we prove that \(\chi _p^\prime (G)\le 9\) for any \(2\)-edge-connected outerplane graph \(G\) with one exception. Moreover, we show that this bound is tight.

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Authors and Affiliations

  1. Department of Applied Mathematics and Business Informatics, Faculty of Economics, Technical University of Košice, Němcovej 32, 040 01, Košice, Slovakia

    Tomáš Bálint & Július Czap

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  1. Tomáš Bálint
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  2. Július Czap
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Correspondence to Július Czap.

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Bálint, T., Czap, J. Facial Parity 9-Edge-Coloring of Outerplane Graphs. Graphs and Combinatorics 31, 1177–1187 (2015). https://doi.org/10.1007/s00373-014-1472-7

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  • DOI: https://doi.org/10.1007/s00373-014-1472-7

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