哈密顿图和欧拉图的一种判别方法

A Distinguishing Method of Hamilton Graphs and Euler Graphs

分析由延长而形成哈密顿回路、欧拉回路的特点,得出求图G(n,m)的最大回路算法:给定始结点xi和始边ei(xj).采用最长路回延长法,对点xi和边ei(xj)分别求最长路回H E序列,在对点xi求最长路回H E序列中,当出现长度为n的点回路的最长项,边ei(xj)出现长度为m的边回路的最长项,或延长后所得路径中没有元素,便结束延长;如对点xi有长度为n的最大点回路最长项,则G(n,m)为哈密顿图;如对边ei(xj)有长度为m的最大边回路最长项,则G(n,m)为欧拉图.

This paper puts forward the concepts of maximal node-cycle, maximal edge-cycle and maximal cycle. Hamilton cycle of graph G（n,rn） is the maximal node-cycle,Euier cycle is the maximal edge-cycle. Analyzing the characteristic of the node cycle and edge cycle by extension, We get the algorithm of the maximal node cycle of G（n,m） . According to the gived initial node xi and initial edge ei（xj） ,Using the longest path-cycle extension algorithm,we get the relevant longest path cycle HE sequence. If there is the. maximal node cycle item, G（n,rn） is Hamilton cycle. If there is the maximal edge-cycle item, G（n,rn） is Euier cycle. The distinguish between Hamilton graph and Euier graph can be generalized the question of maximal node cycle.