Simple Max-Cut for Split-Indifference Graphs and Graphs with Few P4’s
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- Bodlaender H.L., de Figueiredo C.M.H., Gutierrez M., Kloks T., Niedermeier R. (2004) Simple Max-Cut for Split-Indifference Graphs and Graphs with Few P4’s. In: Ribeiro C.C., Martins S.L. (eds) Experimental and Efficient Algorithms. WEA 2004. Lecture Notes in Computer Science, vol 3059. Springer, Berlin, Heidelberg
The simple max-cut problem is as follows: given a graph, find a partition of its vertex set into two disjoint sets, such that the number of edges having one endpoint in each set is as large as possible. A split graph is a graph whose vertex set admits a partition into a stable set and a clique. The simple max-cut decision problem is known to be NP-complete for split graphs. An indifference graph is the intersection graph of a set of unit intervals of the real line. We show that the simple max-cut problem can be solved in linear time for a graph that is both split and indifference. Moreover, we also show that for each constant q, the simple max-cut problem can be solved in polynomial time for (q,q-4)-graphs. These are graphs for which no set of at most q vertices induces more than q-4 distinct P4’s.
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