Abstract
We study the max-cut problem in circulant graphs Cn,r, where Cn,r 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 t-regular cut. The number of edges of a t-regular cut can easily be computed. This gives an O(r log2n) 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.
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