A Note on Finding a Maximum Clique in a Graph Using BDDs

A new approach for the solution of the maximum clique problem for general undirected graphs was presented in the paper titled “Finding the Maximum Clique in a Graph Using BDDs ”, by F.Corno, P.Prinetto and M.Sonza Reorda, in 1993. The approach is based on computing the characteristic function of all the completely connected components in the graph, and then finding the maximum cost satisfying assignment of such a function. The novelty of the method is in the use of Binary Decision Diagrams (BDDs) for representing and manipulating characteristic functions. However, we observe that the algorithm stated does not produce the right answer for certain graphs. In this paper we show how to overcome this inadequacy and improve the algorithm.