Hamiltonian paths in tournament Hamiltonian path: a path visiting every vertex exactly once. Theorem (Szele 1943) There is a tournament on n players with at least n!2-(n-1)Hamiltonian paths.Hamiltonian paths in tournament There is a tournament on n players with at least n!2￾(n￾1) Hamiltonian paths. Theorem (Szele 1943) Hamiltonian path: a path visiting every vertex exactly once