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Tutte theorem : ウィキペディア英語版
Tutte theorem

In the mathematical discipline of graph theory the Tutte theorem, named after William Thomas Tutte, is a characterization of graphs with perfect matchings. It is a generalization of Hall's marriage theorem from bipartite to arbitrary graphs and is a special case of the Tutte–Berge formula.
== Tutte's theorem ==
A graph, , has a perfect matching if and only if for every subset of , the subgraph induced by has at most connected components with an odd number of vertices.〔, p.  84; , Theorem 5.4, p. 76.〕

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