Parameterized algorithms for recognizing monopolar and 2-subcolorable graphs

Iyad Kanj, Christian Komusiewicz, Manuel Sorge, Erik Jan van Leeuwen

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

A graph G is a (ΠAB)-graph if V(G) can be bipartitioned into A and B such that G[A] satisfies property ΠA and G[B] satisfies property ΠB. The (ΠAB)-RECOGNITION problem is to recognize whether a given graph is a (ΠAB)-graph. There are many (ΠAB)-RECOGNITION problems, including the recognition problems for bipartite, split, and unipolar graphs. We present efficient algorithms for many cases of (ΠAB)-RECOGNITION based on a technique which we dub inductive recognition. In particular, we give fixed-parameter algorithms for two NP-hard (ΠAB)-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 (ΠAB)-RECOGNITION.

Original languageEnglish
Pages (from-to)22-47
Number of pages26
JournalJournal of Computer and System Sciences
Volume92
DOIs
StatePublished - 1 Mar 2018
Externally publishedYes

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

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