Panconnectivity for interconnection networks with faulty elements

Let Go and G1 be two graphs with the same vertices. The new graph G（G0, G1; M） is a graph with the vertex set V（0o） ∪）V（G1） and the edge set E（Go） UE（G1） UM, where M is an arbitrary perfect matching between the vertices of Go and G1, i.e., a set of cross edges with one endvertex in Go and the other endvertex in G1. In this paper, we will show that if Go and G1 are f-fault q-panconnected, then for any f 〉 2, G（G0, G1; M） is （f ＋ 1）-fault （q ＋ 2）-panconnected.     

3-正则图的不共边的完美匹配（英文）

研究3-正则图的一个有意义的问题是它是否存在k个没有共边的完美匹配.关于这个问题有一个著名的Fan-Raspaud猜想：每一个无割边的3-正则图都有3个没有共边的完美匹配.但这个猜想至今仍未解决.设dim（P（G））表示图G的完美匹配多面体的维数.本文证明了对于无割边的3-正则图G,如果dim（P（G））≤14,那么k≤4：如果dim（P（G））≤20,那么k≤5.     

与直径和围长有关的图的最大亏格

利用图的直径和围长来研究图的最大亏格的下界,得到了如下结果：设G是直径为d的简单图,若G的围长不小于d（其中d为不小于3的整数）,则ξ（G）≤2,即γM（G）≥1/2β（G）-1．而且,在这种意义下,所得到的界是最好的．     

直径为5的图的2-导出匹配划分和2-导出匹配覆盖问题的NP-完全性

给定一个简单图G和正整数κ,具有完美匹配的图G的κ-导出匹配划分是对顶点集V(C)的一个κ-划分(V1,V2,...,Vκ),其中对每一个i(1≤i≤κ),由Vi导出的G的子图G[Vi]是1-正则的.κ-导出匹配划分问题是指对给定的图G,判定G是否存在一个κ-导出匹配划分.令M1,M2…,Mκ为图G的κ个导出匹配,如果V(M1)UV(M2)∪...∪V(Mκ)=V(G),则我们称{M1,M2,...,Mκ}是G的κ-导出匹配覆盖.κ-导出匹配覆盖问题是指对给定的图G,判定G是否存在κ-导出匹配覆盖.本文给出了Yang,Yuan和Dong所提出问题的解,证明了直径为5的图的导出匹配2一划分问题和导出匹配2-覆盖问题都是NP-完全的.     

单圈共轭图的最小广义Randic指标R-1

图G的广义Randic指标定义为Rα=Rα（G）=∑uv∈E（G）（d（u）d（v））^α,其中d（u）是G的顶点u的度,α是任意实数．本文确定了单圈共轭图的广义Randic指标R-1的严格下界,并刻划了达到最小R-1的极图,这类极图还是化学图．     

ENTIRE CHROMATIC NUMBER AND △-MATCHING OF OUTERPLANE GRAPHS

Let G be an outerplane graph with maximum degree A and the entire chromatic number Xvef（G）. This paper proves that if △ ≥6, then △＋ 1≤Xvef（G）≤△＋ 2, and Xvef （G） = △＋ 1 if and only if G has a matching M consisting of some inner edges which covers all its vertices of maximum degree.     

导出子图和周长的局部定理

设G是n阶2-连通图，3≤c≤n.本文绘出对于图G的每一个同构于K1.3或Z1的导出子图L，若d（u）且如果dL（u，v）=2有（v）=min{，|M3（u）|/2}这里M3（u）={v|dc（u,v）≤3}，则G包含长至少为c的圈．     

M(G,x)≤2的图匹配等价的充要条件

对一个图G,设μ(G,x)表示它的匹配多项式,M(G,x)表示μ(G,x)的最大实数根.令Г_1={G|M(G,x)<2}和Г2={G|M(G,x)≤2}.给出了Г_i(i=1,2)中的两个图G和H匹配等价的充要条件.     

哈密顿线图的一个新结果

设G是一个简单图,G1∈G,G1在G中的度定义为d（G1）=∑v∈V（G）d（v）,其中d（v）为v在G中的度数．主要结果是：设G是n≥3阶几乎无桥的简单连通图,且G≠K（1,n-1）、Q1和Q2,若对G中任何同构于四个顶点路的导出子图I,有d（I）≥2n-6,则G有一个D-闭迹,从而G的线图L（G）是哈密顿图．     

3-正则无爪图的导出匹配覆盖(英文)

The induced matching cover number of a graph G without isolated vertices, denoted by imc（G）,is the minimum integer k such that G has k induced matchings {M1,M2,···,Mk}such that,V（M1）∪V（M2）∪···∪V（Mk）covers V（G）.This paper shows that,if G is a 3-regular claw-free graph,then imc（G）∈{2,3}.     

Rank of maximum matchings in a graph

The matching polytope is the convex hull of the incidence vectors of all (not necessarily perfect) matchings of a graphG. We consider here the problem of computing the dimension of the face of this polytope which contains the maximum cardinality matchings ofG and give a good characterization of this quantity, in terms of the cyclomatic number of the graph and families of odd subsets of the nodes which are always nearly perfectly matched by every maximum matching.This is equivalent to finding a maximum number of linearly independent representative vectors of maximum matchings ofG; the size of such a set is called thematching rank ofG. We also give in the last section a way of computing that rank independently of those parameters.Note that this gives us a good lower bound on the number of those matchings.     

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.     

导出匹配问题的NP-完全性以及导出匹配可扩问题的CO-NP-完全性

图Ｇ的一个匹配Ｍ是导出的,若Ｍ是图Ｇ的一个导出子图。图Ｇ是导邮匹配可扩的（简记ＩＭ－可扩的）,若图Ｇ的任一导出匹配均含于图Ｇ的一个完美匹配当中。本文我们将证明如下结果。⑴对无爪图而言,问题“给定图Ｇ以及一个正整数ｒ,确定是否存在图Ｇ的一个导出匹配Ｍ使得Ｍ≥ｒ”是ＮＰ－完全的。⑵对直径为２的图以及直径为３的偶图,问题“确定一个给定图是否为导出匹配可扩的”是ＣＯ－ＮＰ完全的;而对完全多部图而言,问题“     

Facets of the independent path-matching polytope

Cunningham and Geelen introduced the independent path-matching problem as a common generalization of the weighted matching problem and the weighted matroid intersection problem. Associated with an independent path-matching is an independent path-matching vector. The independent path-matching polytope of an instance of the independent path-matching problem is the convex hull of all the independent path-matching vectors. Cunningham and Geelen described a system of linear inequalities defining the independent path-matching polytope. In this paper, we characterize which inequalities in this system induce facets of the independent path-matching polytope, generalizing previous results on the matching polytope and the common independent set polytope.     

Polyhedral study of the connected subgraph problem

In this paper, we study the connected subgraph polytope which is the convex hull of the solutions to a related combinatorial optimization problem called the maximum weight connected subgraph problem. We strengthen a cut-based formulation by considering some new partition inequalities for which we give necessary and sufficient conditions to be facet defining. Based on the separation problem associated with these inequalities, we give a complete polyhedral characterization of the connected subgraph polytope on cycles and trees.     

The weak global dimension of commutative coherent rings

Let R be a commutative coherent ring and wD(R) denote the weak global dimension of R.We prove that for an integer n≥2 the following are equivalent:.

(a) wD(R)n;.

(b) FP-idM ?Gn-2 for all (FP-)injectives G and for all modules M;.

(c) fdHom(G,M)n-2 for all (FP-)injectives G and for all modules M;.

(d) fdHom(M,G)n-2 for all flat modules G and for all modules M.     

L^2-策略休假下可修的M_1+M_2/G^x(M/G)/1匹配排队系统分析

双输人匹配排队系统是通常排队系统的一种推广．本文对该系统考察了Ｌ２－策略休假和服务台可修的两个重要因素．其中假定系统有两个不同的Ｐｏｉｓｓｏｎ输入，两类顾客按１：１作成一批进行服务，服务台的寿命服从指数分布，服务时间，修理时间和休假时间都服从一般连续型分布，利用向量马氏过程方法，得到了该排队系统的一些重要的稳态排队论指标和可靠性指标．     

与直径和围长有关的最大亏格的下界

本文证明了如下结果:设G为直径为d的简单图,若G的围长不小于d,则当d为不小于4的偶数时,有ξ(G)≤1,即G是上可嵌入的;当d为不小于3的奇数时,有ξ(G)≤2,即γM(G)≥1/2β(G)-1.     

Optimum matching forests III: Facets of matching forest polyhedra

In [3] we presented a linear system which definesP(G), the convex hull of incidence vectors of matching forests of a mixed graphG. However, many of the inequalities of this system may be redundant. Here we describe the dimension of the facets ofP(G) obtained by setting one inequality of the defining system forP(G) to an equation. This leads to a presentation of a minimal defining linear system forP(G), i.e., to a presentation of the facets ofP(G). This generalizes earlier characterizations of facets of 1-matching polyhedra and of branching polyhedra.Research partially supported by a N.R.C. Canada Postdoctorate Fellowship.