A Greedy Probabilistic Heuristic for Graph Black-and-White Anticoloring

Given a graph G and positive integers b and w, the Black-and-White Coloring problem asks about the existence of a partial vertex-coloring of G, with b vertices colored black and w white, such that there is no edge between a black and a white vertex. The problem is known to be NP-complete. In this paper, we deal with the optimization version, mainly for random graphs. Using the method of conditional expectations, we develop a heuristic with a good performance. We also obtain theoretical results on some of the relevant quantities, and compare the performance of the heuristic with that of several others.