2-Colorable Perfect Matching is NP-complete in 2-Connected 3-Regular Planar Graphs
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Author(s)
Demaine, Erik D.
Karntikoon, Kritkorn
Pitimanaaree, Nipun
Date Issued
April 26, 2025
Journal
Theory of Computing Systems
Publisher
Springer US
Citation
Demaine, E.D., Karntikoon, K. & Pitimanaaree, N. 2-Colorable Perfect Matching is NP-complete in 2-Connected 3-Regular Planar Graphs. Theory Comput Syst 69, 22 (2025).
Version
Final published version
Abstract
The 2-colorable perfect matching problem asks whether a graph can be colored with two colors so that each node has exactly one neighbor with the same color as itself. We prove that this problem is NP-complete, even when restricted to 2-connected 3-regular planar graphs. In 1978, Schaefer proved that this problem is NP-complete in general graphs, and claimed without proof that the same result holds when restricted to 3-regular planar graphs. Thus we fill in the missing proof of this claim, while simultaneously strengthening to 2-connected graphs (which implies existence of a perfect matching). We also prove NP-completeness of k-colorable perfect matching, for any fixed k ≥ 2.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s00224-025-10221-2
