Perfect matchings of complete graph
Task number: 3998
Calculate the number of perfect matchings of the complete graph \( K_{2n} \).
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 \(K_{2n}\).
