J. Fiala
The k-in-a-path problem for claw-free graphs
Fiala, J.; Kamiński, M.; Lidický, B.; Paulusma, D.
Abstract
The k-in-a-Path problem is to test whether a graph contains an induced path spanning k given vertices. This problem is NP-complete in general graphs, already when k=3. We show how to solve it in polynomial time on claw-free graphs, when k is an arbitrary fixed integer not part of the input. As a consequence, also the k-Induced Disjoint Paths and the k-in-a-Cycle problem are solvable in polynomial time on claw-free graphs for any fixed k. The first problem has as input a graph G and k pairs of specified vertices (s i ,t i ) for i=1,…,k and is to test whether G contain k mutually induced paths P i such that P i connects s i and t i for i=1,…,k. The second problem is to test whether a graph contains an induced cycle spanning k given vertices. When k is part of the input, we show that all three problems are NP-complete, even for the class of line graphs, which form a subclass of the class of claw-free graphs.
Citation
Fiala, J., Kamiński, M., Lidický, B., & Paulusma, D. (2012). The k-in-a-path problem for claw-free graphs. Algorithmica, 62(1-2), 499-519. https://doi.org/10.1007/s00453-010-9468-z
Journal Article Type | Article |
---|---|
Publication Date | Feb 1, 2012 |
Deposit Date | Dec 6, 2011 |
Publicly Available Date | Jan 16, 2015 |
Journal | Algorithmica |
Print ISSN | 0178-4617 |
Electronic ISSN | 1432-0541 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 62 |
Issue | 1-2 |
Pages | 499-519 |
DOI | https://doi.org/10.1007/s00453-010-9468-z |
Keywords | Induced path, Claw-free graph, Polynomial time algorithm. |
Public URL | https://durham-repository.worktribe.com/output/1501899 |
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Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-010-9468-z
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