In complete graph $K_n$, is it true that we can have at least $2*n$ Hamilton paths?
2026-03-25 10:52:25.1774435945
Hamilton Paths in Complete graph $K_n$
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Since in a complete graph $K_n$ each two vertices are adjacent, the set of Hamiltonian paths of $K_n$ is exactly a set $S_n$ of permutations of its vertices. But $|S_n|=n!$, which is at least $2n$ when $n\ge 3$, but it is less than $2n$ for $n\le 2$.