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Polynomial kernelization for removing induced claws and diamonds
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Cygan, Marek, Pilipczuk, Marcin, Pilipczuk, Michał, van Leeuwen, Erik Jan and Wrochna, Marcin (2015) Polynomial kernelization for removing induced claws and diamonds. In: 41st International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2015), Munich, Germany, 17-19 Jun 2015. Published in: Graph-Theoretic Concepts in Computer Science : 41st International Workshop, WG 2015, Garching, Germany, June 17-19, 2015, Revised Papers, 9224 pp. 450-455. ISBN 9783662531730.
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WRAP_1371795-cs-140815-claw-diamond-deletion.pdf - Accepted Version - Requires a PDF viewer. Download (714Kb) |
Official URL: http://dx.doi.org/10.1007/978-3-662-53174-7_31
Abstract
A graph is called (claw,diamond)-free if it contains neither a claw (a K1,3) nor a diamond (a K4 with an edge removed) as an induced subgraph. Equivalently, (claw,diamond)-free graphs can be characterized as line graphs of triangle-free graphs, or as linear dominoes, i.e., graphs in which every vertex is in at most two maximal cliques and every edge is in exactly one maximal clique.
In this paper we consider the parameterized complexity of the (claw,diamond)-free Edge Deletion problem, where given a graph G and a parameter k, the question is whether one can remove at most k edges from G to obtain a (claw,diamond)-free graph. Our main result is that this problem admits a polynomial kernel. We complement this finding by proving that, even on instances with maximum degree 6, the problem is NP-complete and cannot be solved in time 2o(k)⋅|V(G)|O(1) unless the Exponential Time Hypothesis fail
Item Type: | Conference Item (Paper) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
Library of Congress Subject Headings (LCSH): | Polynomials, Graph theory | ||||
Series Name: | Lecture Notes in Computer Science | ||||
Journal or Publication Title: | Graph-Theoretic Concepts in Computer Science : 41st International Workshop, WG 2015, Garching, Germany, June 17-19, 2015, Revised Papers | ||||
Publisher: | Springer | ||||
ISBN: | 9783662531730 | ||||
Editor: | Mayr , Ernst W. | ||||
Official Date: | 2015 | ||||
Dates: |
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Volume: | 9224 | ||||
Page Range: | pp. 450-455 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 25 May 2016 | ||||
Date of first compliant Open Access: | 6 September 2016 | ||||
Funder: | Narodowe Centrum Nauki [Polish National Science Center] | ||||
Grant number: | DEC-2013/11/D/ST6/03073, DEC-2012/05/D/ST6/03214 | ||||
Conference Paper Type: | Paper | ||||
Title of Event: | 41st International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2015) | ||||
Type of Event: | Conference | ||||
Location of Event: | Munich, Germany | ||||
Date(s) of Event: | 17-19 Jun 2015 | ||||
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