R. Belmonte
The price of connectivity for feedback vertex set
Belmonte, R.; van ’t Hof, P.; Kamiński, M.; Paulusma, D.
Abstract
Let View the MathML source and View the MathML source denote the cardinalities of a minimum feedback vertex set and a minimum connected feedback vertex set of a graph G, respectively. The price of connectivity for feedback vertex set (poc-fvs) for a class of graphs G is defined as the maximum ratio View the MathML source over all connected graphs G∈G. We study the poc-fvs for graph classes defined by a finite family H of forbidden induced subgraphs. We characterize exactly those finite families H for which the poc-fvs for H-free graphs is upper bounded by a constant. Additionally, for the case where ∣H∣=1, we determine exactly those graphs H for which there exists a constant cH such that View the MathML source for every connected H-free graph G, as well as exactly those graphs H for which we can take cH=0.
Citation
Belmonte, R., van ’t Hof, P., Kamiński, M., & Paulusma, D. (2017). The price of connectivity for feedback vertex set. Discrete Applied Mathematics, 217(Part B), 132-143. https://doi.org/10.1016/j.dam.2016.08.011
Journal Article Type | Article |
---|---|
Acceptance Date | Aug 16, 2016 |
Online Publication Date | Sep 17, 2016 |
Publication Date | Jan 30, 2017 |
Deposit Date | Oct 1, 2016 |
Publicly Available Date | Sep 17, 2017 |
Journal | Discrete Applied Mathematics |
Print ISSN | 0166-218X |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 217 |
Issue | Part B |
Pages | 132-143 |
DOI | https://doi.org/10.1016/j.dam.2016.08.011 |
Public URL | https://durham-repository.worktribe.com/output/1375259 |
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Copyright Statement
© 2016 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
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