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An Improved Algorithm for the Nearly Equitable Edge-Coloring Problem
Xuzhen XIE Takao ONO Shin-ichi NAKANO Tomio HIRATA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2004/05/01
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
nearly equitable edge coloring, Euler circuit,
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A nearly equitable edge-coloring of a multigraph is a coloring such that edges incident to each vertex are colored equitably in number. This problem was solved in O(kn2) time, where n and k are the numbers of the edges and the colors, respectively. The running time was improved to be O(n2/k + n|V|) later. We present a more efficient algorithm for this problem that runs in O(n2/k) time.