On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem

Abstract

We study the parameterized complexity of the Bounded-Degree Vertex Deletion problem (BDD), where the aim is to find a maximum induced subgraph whose maximum degree is below a given degree bound. Our focus lies on parameters that measure the structural properties of the input instance. We first show that the problem is W[1]-hard parameterized by a wide range of fairly restrictive structural parameters such as the feedback vertex set number, pathwidth, treedepth, and even the size of a minimum vertex deletion set into graphs of pathwidth and treedepth at most three. We thereby resolve an open question stated in Betzler, Bredereck, Niedermeier and Uhlmann (2012) concerning the complexity of BDD parameterized by the feedback vertex set number. On the positive side, we obtain fixed-parameter algorithms for the problem with respect to the decompositional parameter treecut width and a novel problem-specific parameter called the core fracture number.

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Item Type:	Article
Authors/Creators:	Ganian, R Klute, F Ordyniak, S https://orcid.org/0000-0003-1935-651X
Copyright, Publisher and Additional Information:	© The Author(s) 2020. 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 http://creativecommons.org/licenses/by/4.0/.
Keywords:	Bounded-degree vertex deletion; Feedback vertex set; Parameterized algorithms; Treecut width
Dates:	Accepted: 6 August 2020 Published (online): 19 August 2020 Published: January 2021
Institution:	The University of Leeds
Academic Units:	The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds)
Depositing User:	Symplectic Publications
Date Deposited:	13 Nov 2020 15:31
Last Modified:	28 Apr 2021 07:55
Status:	Published
Publisher:	Springer
Identification Number:	10.1007/s00453-020-00758-8
Related URLs:	Author
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:167889

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On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem

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