Parameterized algorithms for recognizing monopolar and 2-subcolorable graphs

Abstract

A graph G is a (A, B )-graph if V (G) can be bipartitioned into A and B such that G[A] satisfies property A and G[B] satisfies property B . The (A, B )-Recognition problem is to recognize whether a given graph is a (A, B )-graph. There are many (A, B )-Recognition problems, including the recognition problems for bipartite, split,and unipolar graphs. We present efficient algorithms for many cases of (A, B )-Recognitionbased on a technique which we dub inductive recognition. In particular, we givefixed-parameter algorithms for two NP-hard (A, B )-Recognition problems, Monopolar Recognition and 2-Subcoloring, parameterized by the number of maximal cliques in G[A]. We complement our algorithmic results with several hardness results for (A, B )-Recognition.