We define a quantity associated with every vertex in a graph, which we call the Clique Potential and present a number of new heuristic algorithms for graph coloring and the maximum clique problem that use this quantity. The clique potential of a vertex v is defined to be the sum of the degrees of v and its neighbors, and is an approximate measure of whether or not the vertex belongs to a large clique. We also present a recursive method to transform any given graph coloring algorithm into a new algorithm that usually (though not necessarily) uses fewer colors to color a graph than the algorithm from which it was derived. The algorithms run in polynomial time, and experimental evidence shows that they outperform known algorithms, especially on large, dense. graphs. Tests of the algorithms on random graphs of various sizes are presented.
By: T. K. Philips
Published in: RC16326 in 1990
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