Abstract
An edge coloring of a graph G=(V,E) is a function c:E→ℕ that assigns a color c(e) to each edge e∈E such that c(e)≠c(e′) whenever e and e′ have a common endpoint. Denoting S v (G,c) the set of colors assigned to the edges incident to a vertex v∈V, and D v (G,c) the minimum number of integers which must be added to S v (G,c) to form an interval, the deficiency D(G,c) of an edge coloring c is defined as the sum ∑ v∈V D v (G,c), and the span of c is the number of colors used in c. The problem of finding, for a given graph, an edge coloring with a minimum deficiency is NP-hard. We give new lower bounds on the minimum deficiency of an edge coloring and on the span of edge colorings with minimum deficiency. We also propose a tabu search algorithm to solve the minimum deficiency problem and report experiments on various graph instances, some of them having a known optimal deficiency.
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Bouchard, M., Hertz, A. & Desaulniers, G. Lower bounds and a tabu search algorithm for the minimum deficiency problem. J Comb Optim 17, 168–191 (2009). https://doi.org/10.1007/s10878-007-9106-0
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DOI: https://doi.org/10.1007/s10878-007-9106-0