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For questions about matchings in graph theory. A matching on a graph is a set of edges such that no two edges share a common vertex.

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Perfect matchings in infinite graphs

Well, it seems like the following should work: Let us well order $V$ such that for every $v\in V$ set of $u$ such that $u < v$ has cardinality less then $|V|$. Now we are using transfinite induction …
Aleksei Kulikov's user avatar