I形图的匹配等价图类

完全刻画了In以及它的补图的匹配等价图类。     

两类新的匹配唯一性图族

本文研究了具有度序列(13,2S-4,3)的图的匹配唯一性,给出了T(1,4,n)∪(s∪i=0Cpi)(n 4)与T(1,5,n)∪(s∪i=0Cpi)(n 5)及其补图匹配唯一的充要条件.     

几类图的匹配等价图类

两个图G和H的匹配多项式相等,则称它们匹配等价.用[G]表示图G的所有不同构的匹配等价图的集合.刻画了匹配次大根小于1的图及这些图的补图的匹配等价图类.     

最大匹配图的围长

将一个图的所有最大匹配作为顶点集,称两个最大匹配相邻,若它们之一通过交换一条边得到另一个,由引所得图为该图的最大匹配图。本文研究了最大匹配图的围长,从而给出了最大匹配图是树或完全图的条件。     

一类Caterpillars图的匹配刻画

利用匹配多项式的性质以及匹配根的信息研究了图的匹配刻画问题,给出了一类Caterpillars图F（2,m,3）及补图匹配刻画的充分必要条件是m=2,5,8.     

一种最优C—匹配问题

本文以学校招生录取问题为背景提出了一种最优C-匹配问题,证明了关于一个二分图中存在完全C-匹配的充要条件的一个定理,针对问题的不同要求设计了两个最优C-匹配模型和算法,并编制了计算机程序,在招生工作中进行了试验,表明理论和方法都是可行的。     

INDEPENDENT-SET-DELETABLE FACTOR-CRITICAL POWER GRAPHS

It is said that a graph G is independent-set-deletable factor-critical (in short, ID-factor-critical), if, for every independent set 7 which has the same parity as |V(G)|, G-I has a perfect matching. A graph G is strongly IM-extendable, if for every spanning supergraph H of G, every induced matching of H is included in a perfect matching of H. The k-th power of G, denoted by Gk, is the graph with vertex set V(G) in which two vertices are adjacent if and only if they have distance at most k in G. ID-factor-criticality and IM-extendability of power graphs are discussed in this article. The author shows that, if G is a connected graph, then G3 and T(G) (the total graph of G) are ID-factor-critical, and G4 (when |V(G)| is even) is strongly IM-extendable; if G is 2-connected, then D2 is ID-factor-critical.     

对称群上Cayley图的条件匹配排除数

一个图的条件匹配排除数是最少的边的数量,使得从图中删除这些边后形成的图既没有孤立点,也没有完美匹配和几乎完美匹配.条件匹配排除数是衡量网络在边故障情况下的鲁棒性的参数之一.本文给出了对称群上Cayley图的条件匹配排除数.     

一个图的匹配数条件

设G是一个简单图,在图G中任意一个最大匹配的基数叫做G的匹配数,记作v(G),在这篇文章中我们获得了下面的结果,(1)设G是连通的和不完全的,则对于x,y∈v(G)和xyE(G),v(G-{x,y}=v(G)-1的充分必要条件是(a)G[A(G)]是完全的和A(G)的每一个点和C(G)的每一个点相邻,(b)c(D(G))=|A(G)| 1,和(c)y∈D(G-x)对于x,y∈C(G)。(2)设G是连通的和不完全的,则v(G-{x,y})=v(G)-2对于x,y∈V(G)和xyE(G)的充分必要条件是GK_(n,n),其中n≥2。     

匹配多面体的一个性质

证明了若M（G）为图G的匹配多面体,M1,M2为M（G）的两个距离为d的顶点,则M1,M2间有d条内部不相交的最短路．     

T形树的匹配唯一性

研究了T形树T（l1,l2,l3）（l≤l1≤l2≤l3）的匹配唯一性问题。并证明在一定条件下,T（l1,l2,l3）是匹配唯一的．     

两种度序列图的匹配等价图类

刻画了度序列为π(G) ={ 1,3,2 n-2 }和π(G) ={ n - 2 ,n - 4,(n - 3) n-2 }的图 G的匹配等价图类 .     

几类图的匹配唯一性

若图G的匹配多项式为M(G;W),对任何图H,M(G;W)=M(H;W)推出G与H同构,则称G是匹配唯一的.本文讨论了下面的几种图类:(i)B_(m,n,r);(ii)D_(m,n,r);(iii)T_(m,n)的匹配唯一性问题,从而得到一些较为满意的结果.     

On the matching polynomial of subdivision graphs

Let G be a simple graph and let S(G) be the subdivision graph of G, which is obtained from G by replacing each edge of G by a path of length two. In this paper, by the Principle of Inclusion and Exclusion we express the matching polynomial and Hosoya index of S(G) in terms of the matchings of G. Particularly, if G is a regular graph or a semi-regular bipartite graph, then the closed formulae of the matching polynomial and Hosoya index of S(G) are obtained. As an application, we prove a combinatorial identity.     

On matching numbers of tree and bipartite degree sequences

We study the possible values of the matching number among all trees with a given degree sequence as well as all bipartite graphs with a given bipartite degree sequence. For tree degree sequences, we obtain closed formulas for the possible values. For bipartite degree sequences, we show the existence of realizations with a restricted structure, which allows to derive an analogue of the Gale–Ryser Theorem characterizing bipartite degree sequences. More precisely, we show that a bipartite degree sequence has a realization with a certain matching number if and only if a cubic number of inequalities similar to those in the Gale–Ryser Theorem are satisfied. For tree degree sequences as well as for bipartite degree sequences, the possible values of the matching number form intervals.     

BIMATCHING DESIGNS

A collection of k-matchings of bipartite graph Kn1n with the property that every pair of independent edges lies in exactly λ of the k-matchings is called a BIMATCH(n, k, λ)-design. Existences and constructions for various BIMATCH (n, k, λ)-designs are given.     

人寿保险中的投资组合问题

本文考虑与寿险债务匹配的投资组合的一般结构,这种结构中包含了均值-方差有效组合.本文还给出了这种结构中的资产组合的选择和匹配方法以及最优投资组合,并且可以用来确定债务的均值.