Efficient solution for finding Hamilton cycles in undirected graphs

被引：1

作者：

Alhalabi, Wadee ^{[1
]}

Kitanneh, Omar ^{[2
]}

Alharbi, Amira ^{[2
]}

Balfakih, Zain ^{[2
]}

Sarirete, Akila ^{[2
]}

机构：

[1] King Abdulaziz Univ, Fac Comp & Informat Technol, Jeddah, Saudi Arabia

[2] Effat Univ, Coll Engn, Jeddah, Saudi Arabia

来源：

SPRINGERPLUS | 2016年 / 5卷

关键词：

Undirected graphs; Hamiltonian cycle; Necessary condition; Set partition; ALGORITHM;

D O I：

10.1186/s40064-016-2746-8

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页数：14

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