Alecu, B. orcid.org/0000-0002-5515-9145, Atminas, A., Lozin, V. orcid.org/0000-0003-2464-7389 et al. (1 more author) (2023) Combinatorics and Algorithms for Quasi-Chain Graphs. Algorithmica, 85 (3). pp. 642-664. ISSN 0178-4617
Abstract
The class of quasi-chain graphs is an extension of the well-studied class of chain graphs. This latter class enjoys many nice and important properties, such as bounded clique-width, implicit representation, well-quasi-ordering by induced subgraphs, etc. The class of quasi-chain graphs is substantially more complex. In particular, this class is not well-quasi-ordered by induced subgraphs, and the clique-width is not bounded in it. In the present paper, we show that the universe of quasi-chain graphs is at least as complex as the universe of permutations by establishing a bijection between the class of all permutations and a subclass of quasi-chain graphs. This implies, in particular, that the induced subgraph isomorphism problem is NP-complete for quasi-chain graphs. On the other hand, we propose a decomposition theorem for quasi-chain graphs that implies an implicit representation for graphs in this class and efficient solutions for some algorithmic problems that are generally intractable.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2022. 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: | Bipartite graphs; Implicit representation; Polynomial-time algorithm |
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) > Algorithms & Complexity |
Depositing User: | Symplectic Publications |
Date Deposited: | 25 Apr 2024 11:37 |
Last Modified: | 25 Apr 2024 11:37 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00453-022-01019-6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:211810 |