| Title: | Perfect matching cuts partitioning a graph into complementary subgraphs |
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| Authors: | ID Castonguay, Diane (Author)
ID Coelho, Erika M. M. (Author)
ID Coelho, Hebert (Author)
ID Nascimento, Julliano R. (Author)
ID Souza, Uéverton S. (Author) |
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| Files: |  AMC_Castonguay,E.Coelho,H.Coelho,Nascimento,Souza_2025.pdf (420,94 KB)
MD5: 71A89F43C8FD754D6BBD68F737C0444F
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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: | ZUP - University of Primorska Press
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| Abstract: | In PARTITION INTO COMPLEMENTARY SUBGRAPHS (COMP-SUB) we are given a graph G = (V, E), and an edge set property Π, and asked whether G can be decomposed into two graphs, H and its complement H̄, for some graph H, in such a way that the edge cut [V(H), V(H̄)] satisfies the property Π. Motivated by previous work, we consider COMP-SUB(Π) when the property Π=PM specifies that the edge cut of the decomposition is a perfect matching. We prove that COMP-SUB(PM) is GI-hard when the graph G is C_5-free or G is {C_k ≥ 7, C̄_k ≥ 7}-free. On the other hand, we show that COMP-SUB(PM) is polynomial-time solvable on hole-free graphs and on P5-free graphs. Furthermore, we present characterizations of COMP-SUB(PM) on chordal, distance-hereditary, and extended P_4-laden graphs. |
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| Keywords: | graph partitioning, complementary subgraphs, perfect matching, matching cut, graph isomorphism |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 20.03.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 18 str. |
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| Numbering: | Vol. 25, no. 2, [article no.] P2.07 |
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| PID: | 20.500.12556/RUP-21992  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | https://doi.org/10.26493/1855-3974.3015.f4a |
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| Publication date in RUP: | 21.10.2025 |
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| Views: | 202 |
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| Downloads: | 2 |
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