一个求简单图中所有Hamilton回路的算法  

An Algorithm for Finding All Hamiltonian Cycle in Simple Graph

作　　者：文中华[1] 陈志红[2] 

机构地区：[1]湘潭大学信息工程学院,湖南湘潭411105 [2]湘潭大学子弟学校,湖南湘潭411105

出　　处：《湘潭大学自然科学学报》2005年第4期34-41,共8页Natural Science Journal of Xiangtan University

基　　金：湖南省自然科学基金资助项目(02JJY2091)

摘　　要：从Hamilton回路的定义和图的邻接矩阵的定义入手,建立了图中的初级通路的关联关系.利用长度为k的初级通路及其关联关系逐步求长度为k+1的初级通路及其关联关系的方法,求得图的所有Hamilton回路.通过理论分析,说明该算法比已有的求图的所有的Hamilton回路的算法降低了算法的复杂度,为求解Hamilton回路问题提供了新思路.Having started with the definition of Hamiltonian cycle and of the adjacency matrix of a graph, a correlation of path is built in the graph. Through correlation of path in which path＇s length is k, correlation of path in which path＇s length is k ＋ 1 are obtained, step by step, and so we obtain all Hamiltonian cycle. The complexity of algorithm has been reduced, and a new thought for calculating Hamilton cycle problem has been provided.

关 键 词：简单图 HAMILTON回路 关联关系 初级通路 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]