Finding Independent Sets in Unions of Perfect Graphs

Themaximum independent set problem (MAXIS) on general graphs is known to beNPhard to approximate within a factor of n1−ǫ, for any ǫ > 0. However, there are many “easy” classes of graphs on which the problem can be solved in polynomial time. In this context, an interesting question is that of computing the maximum independent set in a graph that can be expressed as the union of a small number of graphs from an easy class. The (MAXIS) problem has been studied on unions of interval graphs and chordal graphs. We study the (MAXIS) problem on unions of perfect graphs (which generalize the above two classes). We present an O( √ n)-approximation algorithm when the input graph is the union of two perfect graphs. We also show that the (MAXIS) problem on unions of two comparability graphs (a subclass of perfect graphs) cannot be approximated within any constant factor.