Cookies

We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.


Durham Research Online
You are in:

Computing small pivot-minors.

Dabrowski, K.K. and Dross, F. and Jeong, J. and Kanté, M.M. and Kwon, O. and Oum, S. and Paulusma, D. (2018) 'Computing small pivot-minors.', in Graph-Theoretic Concepts in Computer Science, 44th International Workshop, WG 2018, Cottbus, Germany, June 27–29, 2018 ; proceedings. Cham, Switzerland: Springer, pp. 125-138. Lecture notes in computer science. (11159).

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.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
Download PDF
(448Kb)
Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/978-3-030-00256-5_11
Publisher statement:The final publication is available at Springer via https://doi.org/10.1007/978-3-030-00256-5_11
Date accepted:15 July 2018
Date deposited:31 July 2018
Date of first online publication:02 September 2018
Date first made open access:No date available

Save or Share this output

Export:
Export
Look up in GoogleScholar