A Polynomial Time Algorithm for Hamilton Cycle Based on the Enlarged Rotation-Extension Technique

Details A Polynomial Time Algorithm for Hamilton Cycle Based on the Enlarged Rotation-Extension Technique A Polynomial Time Algorithm for Hamilton Cycle Based on the Enlarged Rotation-Extension Technique

2010-04-12

arxiv.org/abs/1004.3702v6

Computer Science

Data Structures and Algorithms

10 pages. Compared to our former versions, this version has important improvement. Any specialist can ask for my source code a

Scientific paper

Algorithm studies on the Hamilton cycle are mainly based on the Rotation-Extension method developed by Posa. However, due to the deficiency of Posa's method, all these products are only efficient for much denser graphs or sparse but regular graphs. By many years' study, we developed the "Enlarged Rotation-Extension" technique which utterly changed and expanded the Posa's original one and can surmount its deficiency. Based on this technique, our algorithm can quickly calculate randomly produced un-directed graphs with up to ten thousand vertices on personal computer, no matter dense or sparse, the correctness is one hundred percent. We also calculated the data of hamilton cycles on a famous web site and we still got one hundred percent correctness.

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