共查询到18条相似文献,搜索用时 109 毫秒
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单圈图的邻接矩阵的分类及其最大行列式 总被引:7,自引:3,他引:4
一个单圈图G的邻接矩阵是奇异的当且仅当G含完美匹配和4m(m∈N)阶圈,或G和从G中删去唯一圈中的顶点及其关联边后得到的导出子图均不含完美匹配.单圈图的邻接矩阵的最大行列式是4. 相似文献
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如果对一个简单图G的每一个与G的顶点数同奇偶的独立集I,都有G-I有完美匹配,则称G是独立集可削去的因子临界图.如果图G不是独立集可削去的因子临界图,而对任意两个小相邻的顶点x与y,G xy足独立集可削去的因子临界图,则称G足极大非独立集可削去的因子临界图,本刻画了极大非独立集可削去的因子临界图。 相似文献
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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. 相似文献
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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. 相似文献
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郑茂林 《应用数学与计算数学学报》1987,(2)
ξ1.引言本文所考虑的图均指无自环、无重边、无向有限的连通图,没有特别指明的术语见[1].以V(G)、E(G)分别表示图C的顶点集与边集. 设M是图G的一个支撑子图.若M的每个顶点的度是0或者1,则称M是G的一个匹配,若M是G的匹配中边数最多的一个,则称M是G的一个最大匹配;若M是G的匹配,且M中无0度顶点,则称M是G的一个完美匹配. 图G称为n连通的,若对G的任意两个不同的顶点x,y,G中存在n条以x,y为端点 相似文献
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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 总被引:8,自引:0,他引:8
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“ 相似文献
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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices and neither perfect matchings nor almost-perfect matchings. In this paper, we prove general results regarding the matching preclusion number and the conditional matching preclusion number as well as the classification of their respective optimal sets for regular graphs. We then use these general results to study the problems for Cayley graphs generated by 2-trees and the hyper Petersen networks. 相似文献
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INDEPENDENT-SET-DELETABLE FACTOR-CRITICAL POWER GRAPHS 总被引:3,自引:0,他引:3
原晋江 《数学物理学报(B辑英文版)》2006,26(4):577-584
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. 相似文献
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四角系统是一个二部图,二部图有完美匹配的一个必要条件是对其顶点进行正常着色后,两个色类所含的顶点数相等,然而这一条件并不充分,本文利用构造法证明了两个色类所含顶点数相等却无完美匹配的四角系统的最小阶数是14,并且只有3种非同构的形状,由本文的方法还可以进一步构造出15阶和16阶无完美匹配四角系统的所有非同构形状,它们的数目分别是22与155。 相似文献
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Xiaoyan Jiang Heping Zhang 《Discrete Applied Mathematics》2011,159(15):1581-1593
Let G be a graph that admits a perfect matching M. A forcing set S for a perfect matching M is a subset of M such that it is contained in no other perfect matchings of G. The smallest cardinality of forcing sets of M is called the forcing number of M. Computing the minimum forcing number of perfect matchings of a graph is an NP-complete problem. In this paper, we consider boron-nitrogen (BN) fullerene graphs, cubic 3-connected plane bipartite graphs with exactly six square faces and other hexagonal faces. We obtain the forcing spectrum of tubular BN-fullerene graphs with cyclic edge-connectivity 3. Then we show that all perfect matchings of any BN-fullerene graphs have the forcing number at least two. Furthermore, we mainly construct all seven BN-fullerene graphs with the minimum forcing number two. 相似文献
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The forcing number or the degree of freedom of a perfect matching M of a graph G is the cardinality of the smallest subset of M that is contained in no other perfect matchings of G. In this paper we show that the forcing numbers of perfect matchings in a fullerene graph are not less than 3 by applying the 2-extendability and cyclic edge-connectivity 5 of fullerene graphs obtained recently, and Kotzig’s classical result about unique perfect matching as well. This lower bound can be achieved by infinitely many fullerene graphs. 相似文献
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Domingos M. Cardoso 《Journal of Global Optimization》2001,21(1):91-106
The problem of determining a maximum matching or whether there exists a perfect matching, is very common in a large variety of applications and as been extensively studied in graph theory. In this paper we start to introduce a characterisation of a family of graphs for which its stability number is determined by convex quadratic programming. The main results connected with the recognition of this family of graphs are also introduced. It follows a necessary and sufficient condition which characterise a graph with a perfect matching and an algorithmic strategy, based on the determination of the stability number of line graphs, by convex quadratic programming, applied to the determination of a perfect matching. A numerical example for the recognition of graphs with a perfect matching is described. Finally, the above algorithmic strategy is extended to the determination of a maximum matching of an arbitrary graph and some related results are presented. 相似文献
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Domingos M. Cardoso 《Journal of Global Optimization》2001,19(3):291-306
The problem of determining a maximum matching or whether there exists a perfect matching, is very common in a large variety of applications and as been extensively studied in graph theory. In this paper we start to introduce a characterisation of a family of graphs for which its stability number is determined by convex quadratic programming. The main results connected with the recognition of this family of graphs are also introduced. It follows a necessary and sufficient condition which characterise a graph with a perfect matching and an algorithmic strategy, based on the determination of the stability number of line graphs, by convex quadratic programming, applied to the determination of a perfect matching. A numerical example for the recognition of graphs with a perfect matching is described. Finally, the above algorithmic strategy is extended to the determination of a maximum matching of an arbitrary graph and some related results are presented. 相似文献