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+3 votes
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Is there a way to find no of perfect matchings in a complete graph Kwhere n could be either even or odd..?

asked in Graph Theory by Active (1.4k points)   | 683 views

2 Answers

+7 votes
Best answer

if n is odd then perfect matching 0. because in perfect matching degree of each vertex must be 1, which is not possible if n is odd.

and if n is even then num of perfect matching in K2n=( 2n! ) / ( 2^n  *  n! )

answered by Boss (7.9k points)  
selected by

explain how  K2n=( 2n! ) / ( 2^n  *  n! )

+2 votes
For Kn

if n is odd , then there is no perfect matching.

n is even then you can count it like ->

(n-1) (n-3) (n-5)...1 (This will end in 1 as n is even).
answered by Veteran (42.7k points)  

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