Finding Hamiltonian cycle in polynomial time

Abstract

One of the big mysteries in contemporary computer science is whether P=NP. Finding a Hamiltonian cycle in a graph is one of the classical NP-complete problems. Complexity of the Hamiltonian problem in permutation graphs has been a well-known open problem. No solution exists to get HC in polynomial time and there are no such conditions to decide the probability of HC exists (Neapolitan and Naimipour, 1996). In this study the authors prove that Hamiltonian cycle in an undirected graph can be found in polynomial time, and thus the problem is a discrete problem. Authors present valid conditions to tell in advance, while entering the graph input, that HC does not exist. A polynomial time algorithm for constructing a Hamiltonian cycle is also presented. © 2006 Asian Network for Scientific Information.