Abstract
Let C be a set of colors, and let ω be a cost function which assigns a real number ω(c) to each color C in C. An edge-coloring of a graph G is to color all the edges of G so that any two adjacent edges are colored with different colors. In this paper we give an efficient algorithm to find an optimal edge-coloring of a given tree T, that is, an edge-coloring f of T such that the sum of costs ω(f(e)) of colors f(e) assigned to all edges e is minimum among all edge-colorings of T. The algorithm takes time O(nΔ2) if n is the number of vertices and Δ is the maximum degree of T.
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Zhou, X., Nishizeki, T. Algorithm for the Cost Edge-Coloring of Trees. Journal of Combinatorial Optimization 8, 97–108 (2004). https://doi.org/10.1023/B:JOCO.0000021940.40066.0c
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DOI: https://doi.org/10.1023/B:JOCO.0000021940.40066.0c