North-Holland Max-cut in circulant graphs

We study the max-cut problem in circulant graphs C,,,, where C,,, is a graph whose edge set consists of a cycle of length n and all the vertex pairs of distance r on the cycle. An efficient solution of the problem is obtained so that we show that there is always a maximum cut of a particular shape, called a r-regular cut. The number of edges of a t-regular cut can easily be computed. This gives an O(r log * n) time algorithm for the max-cut. We present also some new classes of facets of the bipartite subgraph polytope and the cut polytope, which are spanned by t-regular cuts. 1. The construction of maximum cut The circulant C,,, is the graph on the vertex set V = { 1,..., n}, and with th