K. K. Dabrowski
Computing small pivot-minors
Dabrowski, K. K.; Dross, F.; Jeong, J.; Kanté, M. M.; Kwon, O.; Oum, S.; Paulusma, D.
Authors
F. Dross
J. Jeong
M. M. Kanté
O. Kwon
S. Oum
Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor
Contributors
A. Brandstädt
Editor
E. Köhler
Editor
K. Meer
Editor
Abstract
A graph G contains a graph H as a pivot-minor if H can be obtained from G by applying a sequence of vertex deletions and edge pivots. Pivot-minors play an important role in the study of rank-width. However, so far, pivot-minors have only been studied from a structural perspective. We initiate a systematic study into their complexity aspects. We first prove that the PIVOT-MINOR problem, which asks if a given graph G contains a given graph H as a pivot-minor, is NP-complete. If H is not part of the input, we denote the problem by H-PIVOT-MINOR. We give a certifying polynomial-time algorithm for H -PIVOT-MINOR for every graph H with |V(H)|≤4|V(H)|≤4 except when H∈{K4,C3+P1,4P1}H∈{K4,C3+P1,4P1}, via a structural characterization of H-pivot-minor-free graphs in terms of a set FHFH of minimal forbidden induced subgraphs.
Citation
Dabrowski, K. K., Dross, F., Jeong, J., Kanté, M. M., Kwon, O., Oum, S., & Paulusma, D. (2018). Computing small pivot-minors. In A. Brandstädt, E. Köhler, & K. Meer (Eds.), Graph-Theoretic Concepts in Computer Science, 44th International Workshop, WG 2018, Cottbus, Germany, June 27–29, 2018 ; proceedings (125-138). https://doi.org/10.1007/978-3-030-00256-5_11
Conference Name | 44th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2018). |
---|---|
Conference Location | Cottbus, Germany |
Start Date | Jun 27, 2018 |
End Date | Jun 29, 2018 |
Acceptance Date | Jul 15, 2018 |
Online Publication Date | Sep 2, 2018 |
Publication Date | Sep 2, 2018 |
Deposit Date | Jul 30, 2018 |
Publicly Available Date | Jul 31, 2018 |
Pages | 125-138 |
Series Title | Lecture notes in computer science |
Series Number | 11159 |
Series ISSN | 0302-9743,1611-3349 |
Book Title | Graph-Theoretic Concepts in Computer Science, 44th International Workshop, WG 2018, Cottbus, Germany, June 27–29, 2018 ; proceedings. |
ISBN | 9783030002558 |
DOI | https://doi.org/10.1007/978-3-030-00256-5_11 |
Public URL | https://durham-repository.worktribe.com/output/1144905 |
Publisher URL | https://www.wg2018.b-tu.de/ |
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Copyright Statement
The final publication is available at Springer via https://doi.org/10.1007/978-3-030-00256-5_11
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