A Polynomial Time Algorithm for Hamilton Cycle (Path)
نویسنده
چکیده
This research develops a polynomial time algorithm for Hamilton Cycle(Path) and proves its correctness. A program is developed according to this algorithm and it works very well. This paper declares the research process, algorithm as well as its proof, and the experiment data. Even only the experiment data is a breakthrough.
منابع مشابه
Minimum cycle factors in quasi-transitive digraphs
We consider the minimum cycle factor problem: given a digraph D, find the minimum number kmin(D) of vertex disjoint cycles covering all vertices of D or verify that D has no cycle factor. There is an analogous problem for paths, known as the minimum path factor problem. Both problems are NP-hard for general digraphs as they include the Hamilton cycle and path problems, respectively. In 1994 Gut...
متن کاملLecturer: Alistair Sinclair Based on Scribe Notes By: 14.1 Finding Hamilton Cycles in Random Graphs
Moreover, there is a polynomial time algorithm to find a Hamilton cycle in a random graph G ∈ Gn,p w.h.p. for all p > lnn+ln lnn+c(n) n , c(n) → ∞ [BFF85]. In this section, we look at a simpler algorithm [AV77] that works for all p ≥ c lnn n−1 for a sufficiently large constant c. This is a slightly weaker result as the value of c, determined by Chernoff bound arguments used in the algorithm’s a...
متن کاملA Polynomial time Algorithm for Hamilton Cycle and Its detailed proof
At present, most effective algorithms to find a Hamilton circle in an undirected graph are generally based on the Rotation-Extension method developed by Posa. However, due to the deficiencies of Posa's method, such algorithms are mostly useful for very dense graphs. This article introduces a method called “Enlarged Rotation-Extension” that modifies and extends Posa's method, overcoming its defi...
متن کاملParameterized TSP: Beating the Average
In the Travelling Salesman Problem (TSP), we are given a complete graph Kn together with an integer weighting w on the edges of Kn, and we are asked to find a Hamilton cycle of Kn of minimum weight. Let h(w) denote the average weight of a Hamilton cycle of Kn for the weighting w. Vizing (1973) asked whether there is a polynomialtime algorithm which always finds a Hamilton cycle of weight at mos...
متن کاملA new constraint of the Hamilton cycle algorithm
Grinberg’s theorem is a necessary condition for the planar Hamilton graphs. In this paper, we use cycle bases and removable cycles to survey cycle structures of the Hamiltonian graphs and derive an equation of the interior faces in Grinberg’s Theorem. The result shows that Grinberg’s Theorem is suitable for the connected and simple graphs. Furthermore, by adding a new constraint of solutions to...
متن کامل