an:00097517
Zbl 0769.05059
Poljak, Svatopluk; Turz??k, Daniel
Max-cut in circulant graphs
EN
Discrete Math. 108, No. 1-3, 379-392 (1992).
00010442
1992
j
05C38 05C85 52B05 05C99 68R10
\(t\)-regular cut; max-cut problem; circulant graphs; cycle; bipartite subgraph polytope; cut polytope
Summary: We study the max-cut problem in circulant graphs \(C_{n,r}\), where \(C_{n,r}\) 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 \(O(r\log^ 2n)\) 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.