An algorithm for finding hamilton cycles in random directed graphs

Abstract

We describe a polynomial ( O( n 1.5)) time algorithm DHAM for finding hamilton cycles in digraphs. For digraphs chosen uniformly at random from the set of digraphs with vertex set {1, 2, …, n} and m = m( n) edges the limiting probability (as n → ∞) that DHAM finds a hamilton cycle equals the limiting probability that the digraph is hamiltonian. Some applications to random “travelling salesman problems” are discussed.