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    Linear time algorithm for computing a small biclique in graphs without long induced paths

    Atminas, A. and Lozin, V. and Razgon, Igor (2012) Linear time algorithm for computing a small biclique in graphs without long induced paths. In: Fomin, F.V. and Kaski, P. (eds.) Algorithm Theory – SWAT 2012. Lecture Notes in Computer Science 7357. Berlin, Germany: Springer Verlag, pp. 142-152. ISBN 9783642311550.

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    Abstract

    The biclique problem asks, given a graph G and a parameter k, whether G has a complete bipartite subgraph of k vertices in each part (a biclique of order k). Fixed-parameter tractability of this problem is a longstanding open question in parameterized complexity that received a lot of attention from the community. In this paper we consider a restricted version of this problem by introducing an additional parameter s and assuming that G does not have induced (i.e. chordless) paths of length s. We prove that under this parameterization the problem becomes fixed-parameter linear. The main tool in our proof is a Ramsey-type theorem stating that a graph with a long (not necessarily induced) path contains either a long induced path or a large biclique.

    Metadata

    Item Type: Book Section
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Sarah Hall
    Date Deposited: 01 Aug 2013 14:57
    Last Modified: 01 Aug 2013 14:57
    URI: http://eprints.bbk.ac.uk/id/eprint/7914

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