What is the number of distinct perfect matchings in a cycle of length $n$ (where $n\ge3$) ?
2026-03-28 21:06:23.1774731983
Number of distinct perfect matchings in a cycle
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Odd number of vertices won't make up for perfect matching. And regarding even number of vertices,for a cycle graph, number of perfect matchings is 2. For a square (cycle graph of 4 vertices) , let's say a is adjacent to b and c. c is adjacent to a and d. d is adjacent to c and b. Now the perfect matching sets are { (a,b) (c,d) } or { (a,c) (b,d) } So we see there are 2 perfect matchings for a cycle graph (C2n). You can try for any cycle length (NOT odd) and find its perfect matching to be 2.