Abstract.
Let G be a simple graph embedded in the surface Σ of Euler characteristic χ(Σ)≥0. Denote χ e (G), Δ and g the edge chromatic number, the maximum degree and the girth of the graph G, respectively. The paper shows that χ e (G)=Δ if Δ≥5 and g≥4, or Δ≥4 and g≥5, or Δ≥3 and g≥9. In addition, if χ(Σ)>0, then χ e (G)=Δ if Δ≥3 and g≥8.
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Acknowledgments. The authors would like to thank Dr. C.Q. Zhang for carefully reading several versions of this paper during its preparation and for suggesting several stylistic changes that have improved the overall presentation.
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Li, X., Luo, R. Edge Coloring of Embedded Graphs with Large Girth. Graphs and Combinatorics 19, 393–401 (2003). https://doi.org/10.1007/s00373-002-0514-8
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DOI: https://doi.org/10.1007/s00373-002-0514-8