A fast algorithm on average for solving the Hamilton Cycle problem

Abstract

We present CertifyHAM, an algorithm which takes as input a graph G and either finds a Hamilton cycle of G or it outputs that such a cycle does not exists. If G ∼ G(n, p) and p ≥ 2000 n then the expected running time of CertifyHAM is O( n p ). This improves upon previous results due to Gurevich and Shelah, Thomason and Alon and Krivelevich.