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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Parameterized Algorithms for Even Cycle Transversal
verfasst von : Pranabendu Misra, Venkatesh Raman, M. S. Ramanujan, Saket Saurabh
Erschienen in: Graph-Theoretic Concepts in Computer Science
Verlag: Springer Berlin Heidelberg
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We consider a decision version of the problem of finding the minimum number of vertices whose deletion results in a graph without even cycles. While this problem is a natural analogue of the
Odd Cycle Transversal
problem (which asks for a subset of vertices to delete to make the resulting graph bipartite), surprisingly this problem is not well studied. We first observe that this problem is NP-complete and give a constant factor approximation algorithm. Then we address the problem in parameterized complexity framework with the solution size
k
as a parameter. We give an algorithm running in time
O
*
(2
O
(
k
)
) for the problem and give an
O
(
k
2
) vertex kernel. (We write
O
*
(
f
(
k
)) for a time complexity of the form
O
(
f
(
k
)
n
O
(1)
), where
f
(
k
) grows exponentially with
k
.)