In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be \({\textsf {NP}}\)-complete. While Matching Cut is trivial for graphs with minimum degree at most one, it is \({\textsf {NP}}\)-complete on graphs with minimum degree two.

中文翻译：

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大最小度数图中的匹配割

在图中，匹配割是作为匹配的边割。匹配割是决定给定图是否有匹配割的问题，已知该割是\({\textsf {NP}}\)-完全的。虽然 Matching Cut 对于最小度数最多为 1 的图是微不足道的，但它在最小度数为 2 的图上是 \({\textsf {NP}}\)-完全的。