An efficient nc algorithm for finding hamiltonian cycles in dense directed graphs

Abstract

Let G be a directed graph with n vertices such that whenever there is no arc from any vertex u to another vertex υ, then the sum of the outdegree of u and the indegree of ν is at least n. It is known that such a graph G always contains a Hamiltonian cycle. We show that such a cycle can be computed with a linear number of processors in O(log3 n) time on a CREW PRAM.