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(LaTeX) 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) $k'\le k$. We also give
a fixed parameter tractable (FPT) algorithm for the problem that runs
in $\Oh(7^{k}k\cdot n^{2})$ time. |
URL for the Abstract: |
http://www.springerlink.com/content/a675490567000012/ |
Keywords: |
Parameterized Algorithms, Kernelization, Pathwidth-One Deletion |
Copyright Message: |
Copyright Springer-Verlag Berlin Heidelberg 2010. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965,
in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law.
Published in the Revised Papers of WG 2010, Crete, Greece, June 28-30, 2010. Lecture Notes in Computer Science, Volume 6410. The original publication is available at www.springerlink.com : http://www.springerlink.com/content/a675490567000012/ |
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