| Title: | On the proper interval completion problem within some chordal subclasses |
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| Authors: | ID Dross, François (Author)
ID Hilaire, Claire (Author)
ID Koch, Ivo (Author)
ID Leoni, Valeria Alejandra (Author)
ID Pardal, Nina (Author)
ID Lopez Pujato, María Inés (Author)
ID Fernandes dos Santos, Vinicius (Author) |
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| Files: |  RAZ_Dross_Francois_2025.pdf (824,75 KB)
MD5: 5C5BFD7A9C8D8F83829B6108263FAF36
 https://doi.org/10.1016/j.disc.2024.114274
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
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| Abstract: | Given a property (graph class) Π, a graph G, and an integer k, the Π-completion problem consists of deciding whether we can turn G into a graph with the property Π by adding at most k edges to G. The Π-completion problem is known to be NP-hard for general graphs when Π is the property of being a proper interval graph (PIG). In this work, we study the PIG-completion problem within different subclasses of chordal graphs. We show that the problem remains NP-complete even when restricted to split graphs. We then turn our attention to positive results and present polynomial time algorithms to solve the PIG-completion problem when the input is restricted to caterpillar and threshold graphs. We also present an efficient algorithm for the minimum co-bipartite-completion for quasi-threshold graphs, which provides a lower bound for the PIG-completion problem within this graph class. |
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| Keywords: | proper interval completion, split graph, threshold graph, quasi-threshold graph, caterpillar |
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| Publication date: | 07.10.2024 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 1-15 |
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| Numbering: | Vol. 348, iss. 1, [article no.] 114274 |
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| PID: | 20.500.12556/RUP-21529  |
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| UDC: | 519.17 |
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| ISSN on article: | 0012-365X |
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| DOI: | 10.1016/j.disc.2024.114274 |
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| COBISS.SI-ID: | 218515203 |
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| Publication date in RUP: | 06.08.2025 |
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| Views: | 390 |
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| Downloads: | 6 |
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