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Edge Colorings of Planar Graphs Without 6-Cycles with Three Chords

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Abstract

A graph G is of class 1 if its edges can be colored with k colors such that adjacent edges receive different colors, where k is the maximum degree of G. It is proved here that every planar graph is of class 1 if its maximum degree is at least 6 and any 6-cycle contains at most two chords.

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Acknowledgments

This work was partially supported by National Natural Science Foundation of China (No. 11271006).

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Wenwen Zhang & Jian-Liang Wu

Authors
  1. Wenwen Zhang
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  2. Jian-Liang Wu
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Correspondence to Jian-Liang Wu.

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Communicated by Sanming Zhou.

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Zhang, W., Wu, JL. Edge Colorings of Planar Graphs Without 6-Cycles with Three Chords. Bull. Malays. Math. Sci. Soc. 41, 1077–1084 (2018). https://doi.org/10.1007/s40840-016-0376-5

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  • DOI: https://doi.org/10.1007/s40840-016-0376-5

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