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.
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 Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Sarah Hall |
| Date Deposited: | 01 Aug 2013 14:57 |
| Last Modified: | 09 Aug 2023 12:34 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/7914 |
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