最大匹配的路变换图

图G的最大匹配的路变换图NM(G)是这样一个图,它以G的最大匹配为顶点,如果两个最大匹配M_1与M_2的对称差导出的图是一条路(长度没有限制),那么M_1和M_2在NM(G)中相邻.研究了这个变换图的连通性,分别得到了这个变换图是一个完全图或一棵树或一个圈的充要条件.     

最大匹配数为|V(G)|+4的Eta图的结构

一个奇圈上加两条奇长的悬挂路组成的图形,称为Eta图.从Eta图的构造出发,研究了最大匹配数为|V(G)|+4的Eta图,得到了10种满足条件的结构.     

具有｜V（G）｜＋2个最大匹配的因子临界图G^＊

在连通图G中,如果对任意的V∈V(G),G-v有完美匹配,则称G是因子临界图.该文刻画了具有|V(G)| +2个最大匹配的因子临界图.进而,刻画了一些特殊的双因子临界图.     

匹配最大根小于等于2的图的匹配等价

给出了十六个匹配等价桥,证明了两个匹配最大根小于等于2的图匹配等价当且仅当它们之间可以由这十六个匹配等价桥进行等价转换,完整地刻画了这些图的补图的匹配等价图类,找到了这些图和它们的补图中的所有匹配唯一图．     

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。     

赋权二部图最大匹配的灵敏分析

本主要从理论上讨论赋权二部图的权的变化对最优解的影响，并在原最大权匹配的基础上给出求解权值变化后的最大权匹配的算法。     

工作分派问题的一种模糊决策模型

针对一类流水线式的工作分派问题,建立了在赋模糊权的二部图中求解模糊最大最小匹配的数学模型,给出了该模型的一个有效算法,并利用模糊决策思想得到了优化此类工作分派问题的一种决策方法     

P_2∪I_m匹配等价类的完整刻画

利用图的匹配多项式及其最大实数根的性质完整刻画了P_2∪I_m的匹配等价类.     

P2UIm匹配等价类的完整刻画

利用图的匹配多项式及其最大实数根的性质完整刻画了P2UIm的匹配等价类.     

子图匹配数与图无符号拉普拉斯谱(英文)

设H是图G的一个子图.图G中同构于H的点不交的子图构成的集合称为G的一个H-匹配.图G的H-匹配的最大基数称为是G的H-匹配数,记为ν(H,G).本文主要研究ν(H,G)与G的无符号拉普拉斯谱的关系,同时也讨论了ν(H,G)与G的拉普拉斯谱的关系.     

Distance Between Two Vertices of Maximum Matching Graphs

The maximum matching graph of a graph has a vertex for each maximum matching and an edge for each pair of maximum matchings which differ by exactly one edge. In this paper, we obtain a lower bound of distance between two vertices of maximum matching graph, and give a necessary and sufficient condition that the bound can be reached.     

Graphs isomorphic to their maximum matching graphs

The maximum matching graph M（G） of a graph G is a simple graph whose vertices are the maximum matchings of G and where two maximum matchings are adjacent in M（G） if they differ by exactly one edge. In this paper, we prove that if a graph is isomorphic to its maximum matching graph, then every block of the graph is an odd cycle.     

A note on minimal matching covered graphs

A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs without isolated vertices contain a perfect matching.     

Maximum Δ‐edge‐colorable subgraphs of class II graphs

A graph G is class II, if its chromatic index is at least Δ + 1. Let H be a maximum Δ‐edge‐colorable subgraph of G. The paper proves best possible lower bounds for |E(H)|/|E(G)|, and structural properties of maximum Δ‐edge‐colorable subgraphs. It is shown that every set of vertex‐disjoint cycles of a class II graph with Δ≥3 can be extended to a maximum Δ‐edge‐colorable subgraph. Simple graphs have a maximum Δ‐edge‐colorable subgraph such that the complement is a matching. Furthermore, a maximum Δ‐edge‐colorable subgraph of a simple graph is always class I. © 2011 Wiley Periodicals, Inc. J Graph Theory     

Characterizations of maximum matching graphs of certain types

The maximum matching graph of a graph G is a graph whose vertices are maximum matchings of G and where two maximum matchings are adjacent in if they differ in exactly one edge. In this paper, the author characterizes the graphs whose maximum matching graphs are regular or cycles, and adds trees to the list of known maximum matching graphs.     

图与超图中的彩色匹配综述

超图H=(V,E)是一个二元组(V,E),其中超边集E中的元素是点集V的非空子集.因此图是一种特殊的超图,超图也可以看作是一般图的推广.特别地,如果超边集E中的元素均是点集V的k元子集,则称该超图为k-一致的.通常情况下,为叙述简便,我们也会将超边简称为边.图(超图)中的匹配是指图(超图)中互不相交的边的集合.对于图(超图)中的彩色匹配,有两种定义方式:一为染色图(超图)中互不相交且颜色不同的边的集合;二为顶点集均为[n]的多个染色图(超图)所构成的集族中互不相交且颜色均不同的边的集合,且每条边均来自集族中不同的图(超图).现主要介绍了图与超图中关于彩色匹配的相关结果.     

Graphs in which some and every maximum matching is uniquely restricted

A matching M in a graph G is uniquely restricted if there is no matching in G that is distinct from M but covers the same vertices as M. Solving a problem posed by Golumbic, Hirst, and Lewenstein, we characterize the graphs in which some maximum matching is uniquely restricted. Solving a problem posed by Levit and Mandrescu, we characterize the graphs in which every maximum matching is uniquely restricted. Both our characterizations lead to efficient recognition algorithms for the corresponding graphs.