Edge Coloring of Embedded Graphs with Large Girth |
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Authors: | Xuechao?Li Email author" target="_blank">Rong?LuoEmail author |
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Institution: | (1) Division of Academic Enhancement, The University of Georgia, Athens, GA 30602, USA;(2) Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA |
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Abstract: | Let G be a simple graph embedded in the surface of Euler characteristic ()0. Denote e(G), and g the edge chromatic number, the maximum degree and the girth of the graph G, respectively. The paper shows that e(G)= if 5 and g4, or 4 and g5, or 3 and g9. In addition, if ()>0, then e(G)= if 3 and g8.
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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Keywords: | Edge coloring Edge chromatic number Euler contribution |
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