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.
Highlights
Introduction and preliminaries TheHamiltonian cycle (HC) problem has many applications such as time scheduling, the choice of travel routes and network topology (Bollobas et al 1987; Akhmedov and Winter 2014)
Resolving the HC is an important problem in graph theory and computer science as well (Pak and Radoičić 2009)
There is an algorithm for solving the HC problem with polynomial expected running time (Bollobas et al 1987)
Summary
Introduction and preliminaries TheHamiltonian cycle (HC) problem has many applications such as time scheduling, the choice of travel routes and network topology (Bollobas et al 1987; Akhmedov and Winter 2014). Dirac’s theorem A simple graph with n vertices in which each vertex has degree at least⌈n/2⌉has a Hamiltonian cycle.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
