Abstract
We consider the problem of orienting the edges of a graph so that the length of a longest path in the resulting digraph is minimum. As shown by Gallai, Roy and Vitaver, this edge orienting problem is equivalent to finding the chromatic number of a graph. We study various properties of edge orienting methods in the context of local search for graph coloring. We then exploit these properties to derive four tabu search algorithms, each based on a different neighborhood. We compare these algorithms numerically to determine which are the most promising and to give potential research directions.
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Gendron, B., Hertz, A. & St-Louis, P. On edge orienting methods for graph coloring. J Comb Optim 13, 163–178 (2007). https://doi.org/10.1007/s10878-006-9019-3
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DOI: https://doi.org/10.1007/s10878-006-9019-3