2-Colorable Perfect Matching is NP-complete in 2-Connected 3-Regular Planar Graphs
Erik D. DemaineKritkorn KarntikoonNipun Pitimanaaree
Erik D. DemaineKritkorn KarntikoonNipun Pitimanaaree
Sep 2023
0被引用
0笔记
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摘要原文
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 $k \geq 2$.
