2类图完美匹配数目的解析式  

The analytic formula of the number of perfect matchings of two types of graphs

作　　者：唐保祥[1] 任韩[2] 

机构地区：[1]天水师范学院数学与统计学院,甘肃天水741001 [2]华东师范大学数学系,上海200062

出　　处：《中山大学学报（自然科学版）》2016年第4期15-17,共3页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(11171114)

摘　　要：匹配计数理论是图论研究的重要内容之一,而且是一个有生机和活力的研究领域。它不仅有很强的应用背景,而且在过去的几十年中,它是快速发展的组合论中许多重要思想的源泉。但是,一般图的完美匹配计数问题却是NP-难问题。用划分,求和,再递推的方法给出了2类图完美匹配数目的计算公式,所给出的方法,可以计算出许多类图的所有完美匹配的数目。Matching counting theory is an important part of graph theory and also a active research field.It has not only many applications background,and also the source of many important ideas developed during the rapid growth of combinatorics during the last several decades. But the problem of counting the number of perfect matchings for general graphs is NP-hard. By applying differentiation,summation and re-recursion calculation,several counting formulas of the perfect matchings for two specific types of graphs are given. By the method presented in this paper,the number of all perfect matchings of many graphs can be calculated.

关 键 词：完美匹配 梯子 线性递推式 特征方程 

分 类 号：O157.5[理学—数学]