Chakraborty, D. orcid.org/0000-0003-0534-6417, Gajjar, K. and Rusu, I. (2024) Recognizing geometric intersection graphs stabbed by a line. Theoretical Computer Science, 995. 114488. ISSN 0304-3975
Abstract
In this paper, we determine the computational complexity of recognizing two graph classes, grounded -graphs and stabbable grid intersection graphs. An -shape is made by joining the bottom end-point of a vertical (|) segment to the left end-point of a horizontal (−) segment. The top end-point of the vertical segment is known as the anchor of the -shape. Grounded -graphs are the intersection graphs of -shapes such that all the -shapes' anchors lie on the same horizontal line. We show that recognizing grounded -graphs is -complete. This answers an open question asked by Jelínek & Töpfer (Electron. J. Comb., 2019).
Grid intersection graphs are the intersection graphs of axis-parallel line segments in which two vertical (similarly, two horizontal) segments cannot intersect. We say that a (not necessarily axis-parallel) straight line ℓ stabs a segment s, if s intersects ℓ. A graph G is a stabbable grid intersection graph (Image 1) if there is a grid intersection representation of G in which the same line stabs all its segments. We show that recognizing Image 1 graphs is -complete, even on a restricted class of graphs. This answers an open question asked by Chaplick et al. (Order, 2018).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 Elsevier B.V. This is an author produced version of an article published in Theoretical Computer Science. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Intersection graph, Grounded L-graph, Stabbable grid intersection graph, Complexity, NP-completeness |
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: | 08 Mar 2024 15:26 |
Last Modified: | 06 Mar 2025 01:13 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.tcs.2024.114488 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:210062 |
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