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, June). Computing small pivot-minors. Presented at 44th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2018)., Cottbus, Germany
Presentation Conference Type | Conference Paper (Published) |
---|---|
Conference Name | 44th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2018). |
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 |
Print ISSN | 0302-9743 |
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/ |
Files
Accepted Conference Proceeding
(459 Kb)
PDF
Copyright Statement
The final publication is available at Springer via https://doi.org/10.1007/978-3-030-00256-5_11
You might also like
Computing balanced solutions for large international kidney exchange schemes
(2024)
Journal Article
An Algorithmic Framework for Locally Constrained Homomorphisms
(2024)
Journal Article
Matching cuts in graphs of high girth and H-free graphs
(2023)
Presentation / Conference Contribution
Solving problems on generalized convex graphs via mim-width
(2023)
Journal Article
Dichotomies for Maximum Matching Cut: H-Freeness, Bounded Diameter, Bounded Radius
(2023)
Presentation / Conference Contribution
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search