Parameterized complexity of the weighted independent set problem beyond graphs of bounded clique number

Authors:
Konrad Dabrowski;Vadim Lozin;Haiko Müller;Dieter Rautenbach
Affiliations:
DIMAP & Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK;DIMAP & Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK;School of Computing, University of Leeds, Leeds LS2 9JT, UK;Institut für Optimierung und Operations Research, Universität Ulm, Ulm, Germany
Venue:
Journal of Discrete Algorithms
Year:
2012

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Abstract

The maximum independent set problem is known to be NP-hard for graphs in general, but is solvable in polynomial time for graphs in many special classes. It is also known that the problem is generally intractable from a parameterized point of view. A simple Ramsey argument implies the fixed-parameter tractability of the maximum independent set problem in classes of graphs of bounded clique number. Beyond this observation very little is known about the parameterized complexity of the problem in restricted graph families. In the present paper we develop fpt-algorithms for graphs in some classes extending graphs of bounded clique number.