Bonnet, É, Chakraborty, D. orcid.org/0000-0003-0534-6417 and Duron, J. (2024) Cutting Barnette graphs perfectly is hard. Theoretical Computer Science, 1010. 114701. ISSN 0304-3975
Abstract
A perfect matching cut is a perfect matching that is also a cutset, or equivalently, a perfect matching containing an even number of edges on every cycle. The corresponding algorithmic problem, Perfect Matching Cut, is known to be NP-complete in subcubic bipartite graphs [Le & Telle, TCS '22], but its complexity was open in planar graphs and cubic graphs. We settle both questions simultaneously by showing that Perfect Matching Cut is NP-complete in 3-connected cubic bipartite planar graphs or Barnette graphs. Prior to our work, among problems whose input is solely an undirected graph, only Distance-2 4-Coloring was known to be NP-complete in Barnette graphs. Notably, Hamiltonian Cycle would only join this private club if Barnette's conjecture were refuted.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | Perfect matching; Cutset; Perfect matching set; Planar graphs; Barnette graphs; 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) > Algorithms & Complexity |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Jul 2024 10:46 |
Last Modified: | 09 Jul 2024 10:46 |
Published Version: | https://www.sciencedirect.com/science/article/pii/... |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.tcs.2024.114701 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:214059 |
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