Koch, I., Pardal, N. orcid.org/0000-0002-5150-6947 and dos Santos, V.F. (2024) Edge deletion to tree-like graph classes. Discrete Applied Mathematics, 348. pp. 122-131. ISSN 0166-218X
Abstract
For a fixed property (graph class) Π, given a graph G and an integer k, the Π-deletion problem consists in deciding if we can turn G into a graph with the property Π by deleting at most k edges. The Π-deletion problem is known to be NP-hard for most of the well-studied graph classes, such as chordal, interval, bipartite, planar, comparability and permutation graphs, among others; even deletion to cacti is known to be NP-hard for general graphs. However, there is a notable exception: the deletion problem to trees is polynomial. Motivated by this fact, we study the deletion problem for some classes similar to trees, addressing in this way a knowledge gap in the literature. We prove that deletion to cacti is hard even when the input is a bipartite graph. On the positive side, we show that the problem becomes tractable when the input is chordal, and for the special case of quasi-threshold graphs we give a simpler and faster algorithm. In addition, we present sufficient structural conditions on the graph class Π that imply the NP-hardness of the Π-deletion problem, and show that deletion from general graphs to some well-known subclasses of forests is NP-hard.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | Edge deletion problems; Modification problems; Sparse graph classes |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 13 Feb 2024 12:31 |
Last Modified: | 13 Feb 2024 12:31 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.dam.2024.01.028 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:209134 |