title: Efficient solution for finding Hamilton cycles in undirected graphs.
abstract: The Hamilton cycle problem is closely related to a series of famous problems and puzzles (traveling salesman problem, Icosian game) and, due to the fact that it is NP-complete, it was extensively studied with different algorithms to solve it. The most efficient algorithm is not known. In this paper, a necessary condition for an arbitrary un-directed graph to have Hamilton cycle is proposed. Based on this condition, a mathematical solution for this problem is developed and several proofs and an algorithmic approach are introduced. The algorithm is successfully implemented on many Hamiltonian and non-Hamiltonian graphs. This provides a new effective approach to solve a problem that is fundamental in graph theory and can influence the manner in which the existing applications are used and improved.
authors: Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia.
authors: Wadee
authors: W
authors: Alhalabi
authors: College of Engineering, Effat University, Jeddah, Saudi Arabia.
authors: Omar
authors: O
authors: Kitanneh
authors: College of Engineering, Effat University, Jeddah, Saudi Arabia.
authors: Amira
authors: A
authors: Alharbi
authors: College of Engineering, Effat University, Jeddah, Saudi Arabia.
authors: Zain
authors: Z
authors: Balfakih
authors: College of Engineering, Effat University, Jeddah, Saudi Arabia.
authors: Akila
authors: A
authors: Sarirete
keywords: Hamiltonian cycle; Necessary condition; Set partition; Undirected graphs