A Fast Algorithm for Computing a Nearly Equitable Edge Coloring with Balanced Conditions
We discuss the nearly equitable edge coloring problem on a multigraph and propose an efficient algorithm for solving the problem, which has a better time complexity than the previous algorithms. The coloring computed by our algorithm satisfies additional balanced conditions on the number of edges used in each color class, where conditions are imposed on the balance among all edges in the multigraph as well as the balance among parallel edges between each vertex pair. None of the previous algorithms are guaranteed to satisfy these balanced conditions simultaneously.
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- 4.Hilton, A.J.W., de Werra, D.: Sufficient conditions for balanced and for equitable edge-colouring of graphs. O.R. Working paper 82/3, Département de Mathématiques, École Polytechnique Fédérate de Lausanne, Switzerland (1982)Google Scholar
- 7.Nakano, S., Suzuki, Y., Nishizeki, T.: An algorithm for the nearly equitable edge-coloring of graphs. IEICE Trans. Inf. & Syst. J78-D-I, 437–444 (1995) (in Japanese)Google Scholar
- 9.de Werra, D.: Equitable colorations of graphs. Revue française d’Informatique et de Recherche Operationelle R-3, pp. 3–8 (1971)Google Scholar
- 10.Xie, X., Ono, T., Nakano, S., Hirata, T.: An improved algorithm for the nearly equitable edge-coloring problem. IEICE Trans. Fund. E87-A, 1029–1033 (2004)Google Scholar