Efficient solution for finding Hamilton cycles in undirected graphs

Springerplus. 2016 Jul 28;5(1):1192. doi: 10.1186/s40064-016-2746-8. eCollection 2016.


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.

Keywords: Hamiltonian cycle; Necessary condition; Set partition; Undirected graphs.