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Perfect matchings of complete graph

Task number: 3998

Calculate the number of perfect matchings of the complete graph K2n.

  • Solution

    The perfect matchings of the complete graph correspond to the partition of the 2n element set into pairs, regardless of the order of these pairs.

  • Answer

    There are (2n-1)(2n-3)\ldots\cdot 3 {\cdot} 1=n!\binom{2n}{2{,}2,…,2} perfect matchings of K_{2n}.

Difficulty level: Easy task (using definitions and simple reasoning)
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