On edge orienting methods for graph coloring

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.

• Type: Journal
• Year: 2007
• Where: JCO
• Authors: Bernard Gendron, Alain Hertz, Patrick St-Louis
• Keywords: Chromatic Number, Edge Orienting Methods, JCO 2007, Longest Path