Simple Max-Cut for Split-Indifference Graphs and Graphs with Few P4's
نویسندگان
چکیده
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. AMS classification: 68Q25, 05C85, 05C17.
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