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On the use of some known methods for \(T\)-colorings of graphs. (English) Zbl 0771.68089

Summary: A generalization of the classical graph coloring model is studied in this paper. The problem we are interested in is a variant of the general \(T\)- coloring problem related in the literature. We want to color the vertices of a graph in such a way that the two colors assigned to two adjacent vertices \(i\) and \(j\) differ by at least \(t_{ij}\), where \(t_{ij}\) is a fixed coefficient associated to the edge \([i,j]\). The goal is to minimize the length of the spectrum of colors used. We present here the results produced by well-known heuristics ( tabu search and simulated annealing) applied to the considered problem. The results are compared with optimal colorings obtained by a branch-and-bound algorithm.

MSC:

68R10 Graph theory (including graph drawing) in computer science
05C15 Coloring of graphs and hypergraphs
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