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:

On cycle transversals and their connected variants in the absence of a small linear forest.

Dabrowski, K.K. and Feghali, C. and Johnson, M. and Paesani, G. and Paulusma, D. and Rzążewski, P. (2020) 'On cycle transversals and their connected variants in the absence of a small linear forest.', Algorithmica., 82 (10). pp. 2841-2866.


A graph is H-free if it contains no induced subgraph isomorphic to H. We prove new complexity results for the two classical cycle transversal problems FEEDBACK VERTEX SET and ODD CYCLE TRANSVERSAL by showing that they can be solved in polynomial time on (sP1+P3)-free graphs for every integer s≥1. We show the same result for the variants CONNECTED FEEDBACK VERTEX SET and CONNECTED ODD CYCLE TRANSVERSAL. We also prove that the latter two problems are polynomial-time solvable on cographs; this was already known for FEEDBACK VERTEX SET and ODD CYCLE TRANSVERSAL. We complement these results by proving that ODD CYCLE TRANSVERSAL and CONNECTED ODD CYCLE TRANSVERSAL are NP-complete on (P2+P5,P6)-free graphs.

Item Type:Article
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
File format - PDF
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution.
Download PDF (Advance online version)
Publisher Web site:
Publisher statement:This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Date accepted:26 March 2020
Date deposited:21 April 2020
Date of first online publication:29 April 2020
Date first made open access:13 May 2020

Save or Share this output

Look up in GoogleScholar