Parameterized Algorithms for Recognizing Monopolar and 2-Subcolorable Graphs [article]

Iyad Kanj, Christian Komusiewicz, Manuel Sorge, Erik Jan van Leeuwen
2018 arXiv   pre-print
A graph G is a (Π_A,Π_B)-graph if V(G) can be bipartitioned into A and B such that G[A] satisfies property Π_A and G[B] satisfies property Π_B. The (Π_A,Π_B)-Recognition problem is to recognize whether a given graph is a (Π_A,Π_B)-graph. There are many (Π_A,Π_B)-Recognition problems, including the recognition problems for bipartite, split, and unipolar graphs. We present efficient algorithms for many cases of (Π_A,Π_B)-Recognition based on a technique which we dub inductive recognition. In
more » ... cular, we give fixed-parameter algorithms for two NP-hard (Π_A,Π_B)-Recognition problems, Monopolar Recognition and 2-Subcoloring. We complement our algorithmic results with several hardness results for (Π_A,Π_B)-Recognition.
arXiv:1702.04322v2 fatcat:iv2zl54wrzadfa7dx3d4rpcuuq