SIMPLE MAX-CUT for split-indifference graphs and graphs with Few P4's

Abstract

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. © Springer-Verlag 2004.