Thomassé, S, Trotignon, N and Vušković, K (2014) A polynomial turing-Kernel for weighted independent set in bull-free graphs. In: Kratsch, D and Todinca, I, (eds.) Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science. Springer Verlag , 408 - 419. ISBN 9783319123394
Abstract
The maximum stable set problem is NP-hard, even when restricted to triangle-free graphs. In particular, one cannot expect a polynomial time algorithm deciding if a bull-free graph has a stable set of size k, when k is part of the instance. Our main result in this paper is to show the existence of an FPT algorithm when we parameterize the problem by the solution size k. A polynomial kernel is unlikely to exist for this problem. We show however that our problem has a polynomial size Turing-kernel. More precisely, the hard cases are instances of size O(k5). All our results rely on a decomposition theorem of bull-free graphs due to Chudnovsky which is modified here, allowing us to provide extreme decompositions, adapted to our computational purpose.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2014, Springer Verlag. This is an author produced version of a paper published in Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-12340-0_34 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 Jan 2015 09:48 |
Last Modified: | 28 Oct 2015 02:15 |
Published Version: | http://dx.doi.org/10.1007/978-3-319-12340-0_34 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/978-3-319-12340-0_34 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:82507 |