A linear-time algorithm for finding Hamiltonian cycles in tournaments

Abstract

We give a simple algorithm to transform a Hamiltonian path in a Hamiltonian cycle, if one exists, in a tournament T of order n. Our algorithm is linear in the number of arcs, i.e., of complexity O( m)=O( n 2) and when combined with the O( n log n) algorithm of [2] to find a Hamiltonian path in T, it yields an O( n 2) algorithm for searching a Hamiltonian cycle in a tournament. Up to now, algorithms for searching Hamiltonian cycles in tournaments were of order O( n 3) [3], or O( n 2 log n) [5].