## Abstract

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 particular, we give fixed-parameter algorithms for two NP-hard (Π_{A},Π_{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 (Π_{A},Π_{B})-RECOGNITION.

Original language | English |
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Pages (from-to) | 22-47 |

Number of pages | 26 |

Journal | Journal of Computer and System Sciences |

Volume | 92 |

DOIs | |

State | Published - 1 Mar 2018 |

Externally published | Yes |

## Keywords

- Fixed-parameter algorithms
- Graph classes
- Monopolar graphs
- Split graphs
- Subcolorings
- Unipolar graphs
- Vertex-partition problems

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics