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  A Quartic Kernel for Pathwidth-One Vertex Deletion

Philip, G., Raman, V., & Villanger, Y. (2010). A Quartic Kernel for Pathwidth-One Vertex Deletion. In D. M. Thilikos (Ed.), Graph Theoretic Concepts in Computer Science (pp. 196-207). Berlin: Springer. doi:10.1007/978-3-642-16926-7_19.

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 Creators:
Philip, Geevarghese1, Author           
Raman, Venkatesh1, Author
Villanger, Yngve1, Author
Affiliations:
1External Organizations, ou_persistent22              

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 Abstract: The pathwidth of a graph is a measure of how path-like the graph is. Given a graph G and an integer k, the problem of finding whether there exist at most k vertices in G whose deletion results in a graph of pathwidth at most one is \npc{}. We initiate the study of the parameterized complexity of this problem, parameterized by k. We show that the problem has a quartic vertex-kernel: We show that, given an input instance (G=(V,E),k);|V|=n, we can construct, in polynomial time, an instance (G',k') such that (i) (G,k) is a YES instance if and only if (G',k') is a YES instance, (ii) G' has \Oh(k^4}) vertices, and (iii) k'≤ k. We also give a fixed parameter tractable (FPT) algorithm for the problem that runs in \Oh(7^{kk⋅ n²) time.

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Language(s): eng - English
 Dates: 20102010
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: DOI: 10.1007/978-3-642-16926-7_19
BibTex Citekey: PhilipRamanVillanger2010
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Title: WG 2010
Place of Event: Crete, Greece
Start-/End Date: 2010-06-28 - 2010-06-30

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Title: Graph Theoretic Concepts in Computer Science
  Abbreviation : WG 2010
  Subtitle : 36th International Workshop, WG 2010, Zarós, Crete, Greece, June 28-30, 2010 Revised Papers
Source Genre: Proceedings
 Creator(s):
Thilikos, Dimitrios M.1, Editor
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: Berlin : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 196 - 207 Identifier: ISBN: 978-3-642-16925-0

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Title: Lecture Notes in Computer Science
  Abbreviation : LNCS
Source Genre: Series
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Pages: - Volume / Issue: 6410 Sequence Number: - Start / End Page: - Identifier: -