A single exponential-time FPT algorithm for cactus contraction

For a collection F of graphs, the F-Contraction problem takes a graph G and an integer k as input and decides if G can be modified to some graph in F using at most k edge contractions. The F-Contraction problem is NP-Complete for several graph classes F. Heggernes et al. (2014) [4] initiated the stu...

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Bibliographic Details
Published in:	Theoretical computer science Vol. 954; p. 113803
Main Authors:	Krithika, R., Misra, Pranabendu, Tale, Prafullkumar
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 18.04.2023
Subjects:	Cactus graphs Fixed parameter tractable algorithms Graph contraction Fixed parameter tractable algorithms Cactus graphs Graph contraction
ISSN:	0304-3975, 1879-2294
Online Access:	Get full text
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Summary:	For a collection F of graphs, the F-Contraction problem takes a graph G and an integer k as input and decides if G can be modified to some graph in F using at most k edge contractions. The F-Contraction problem is NP-Complete for several graph classes F. Heggernes et al. (2014) [4] initiated the study of F-Contraction in the realm of parameterized complexity. They showed that it is FPT if F is the set of all trees or the set of all paths. In this paper, we study F-Contraction where F is the set of all cactus graphs and show that we can solve it in 2O(k)⋅\|V(G)\|O(1) time.
ISSN:	0304-3975 1879-2294
DOI:	10.1016/j.tcs.2023.113803