Chakraborty, D. orcid.org/0000-0003-0534-6417, Das, S., Francis, M.C. orcid.org/0000-0002-0498-7856 et al. (1 more author) (Cover date: 31 January 2021) On rectangle intersection graphs with stab number at most two. Discrete Applied Mathematics, 289. pp. 354-365. ISSN 0166-218X
Abstract
Rectangle intersection graphs are the intersection graphs of axis-parallel rectangles in the plane. A graph G is said to be a k-stabbable rectangle intersection graph, or k-SRIG for short, if it has a rectangle intersection representation in which k horizontal lines can be placed such that each rectangle intersects at least one of them. In this article, we introduce some natural subclasses of 2-SRIG and study the containment relationships among them. It is shown that one of these subclasses can be recognized in linear-time if the input graphs are restricted to be triangle-free. We also make observations about the chromatic number of 2-SRIGs. It is shown that the Chromatic Number problem is NP-complete for 2-SRIGs, by showing that the problem is NP-complete for 2-row B0-VPGs. This is a strengthening of some known results from the literature.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020, Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/. This is an author produced version of an article published in Discrete Applied Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Rectangle intersection graph; Stab number; Chromatic number |
Dates: |
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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: | 01 Sep 2023 08:11 |
Last Modified: | 12 Oct 2023 13:40 |
Published Version: | https://www.sciencedirect.com/science/article/pii/... |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.dam.2020.11.003 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:202891 |
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