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关于图的最大匹配问题的若干结果

The study on the maximum matchings (as well as perfect matchings) of a graph plays a central role in matching theory. In addition to the algorithnis of finding maximum matchings, the structural properties of all maximum matchings are significant in theory or application aspect. Roughly speaking, the properties we are concerned in this thesis are mainly as follows:1. How many maximum matchings are there in a graph?2.  (本文共107页) 本文目录 | 阅读全文>>

《郑州大学学报(自然科学版)》2000年03期
郑州大学学报(自然科学版)

关于图的最大匹配问题的若干结果

最大匹配问题是匹配理论中核心问题之一 ,它广泛应用在组合优化、线性规划、理论化学与量子化学等领域 .当前人们关于这一问题的研究主要集中在当图有完美匹配时的情况 ,但对图无完美匹配的情况相应的研究工作却很少 .因此我们将这一研究领域推广到无完美匹配的图上 ,研究了与图的最大匹配有关的一些问题 ,主要结果如下 :首先研究并给出了具有正盈量的二部图与因子临界图的最大匹配数的可达下界 ,并完全解决了一些特殊图的最大匹配计数问题 .我们知道完美匹配的计数问题是 ...  (本文共1页) 阅读全文>>

《数学季刊》2013年03期
数学季刊

Factor-critical 图的阈值(英文)

§1.IntroductionThere are two basic models of random graphs,the binomial model and uniform model.Given a real number p,0≤p≤1,the binomial random graph,denoted by G(n,p),isdefined by taking as the set of all graphs on vertex set[n]={1,2,···,n}and settingP(G)=peG(1 p)(n2)eG,where eG=|E(G)|stands for the number of edges of G.Thebinomial model is a special case of a reliability network(In this more general model,is thefam...  (本文共11页) 阅读全文>>

《Science China(Information Sciences)》2014年07期
Science China(Information Sciences)

On the parameterized vertex cover problem for graphs with perfect matching

1 IntroductionThe vertex cover problem is a classical NP-complete problem[1],with important applications in fieldssuch as computational biochemistry[2,3].Various computational approaches to the problem,includingapproximation algorithms(see the survey article[4])and parameterized algorithms[5–8],have beenextensively studied.An approximation algorithm of ratio 2 for the problem can be easily achieved basedon graph maxi...  (本文共12页) 阅读全文>>

《Journal of Shanghai University(English Edition)》2011年06期
Journal of Shanghai University(English Edition)

Results on energies for trees with a given diameter having perfect matching

IntroductionThe total energy of all π-electrons in conjugatedmolecules, within the framework of Hu¨ckel molecularorbital (HMO) approximation, is a well-known topolog-ical index in theoretical chemistry. It is in good linearcorrelation with experimental heats of formation of con-jugated hydrocarbons[1]. Motivated by this reason, anumber of results have been reached for the orderingof graphs with extremal energies, whi...  (本文共8页) 阅读全文>>

《Science Bulletin》1987年21期
Science Bulletin

UNIQUE FACTOR GRAPHS WITH MAXIMAL NUMBER OF EDGES

LetG~(V,E)be a simple graph,toLethaveF be::ubset of ed爸es. IfFthenFCOVerS V认all thethe vertex set and E thevertices of G and any two edgeedgesSetinFnO CO幻On1ODif G hasend vertex15 ealled a faetorOfaPerfeet matehingof‘.Obvi-Ously, Ina faetor.then the number of its vertices!Vl,mustb。even.the Present rePort,the graPhs are eharaeterized to haveProPer-tOofties:(i)they have only one faetor,and(11)the nutnber of edges 15the...  (本文共3页) 阅读全文>>

《Wuhan University Journal of Natural Sciences》2015年01期
Wuhan University Journal of Natural Sciences

Matching Preclusion for Augmented k-ary n-cubes

0 IntroductionA matching in a graph is a set of pairwisenonadjacent edges.A perfect matching in a graph is a setof edges such that every vertex is incident with exactlyone edge in this set.An almost-perfect matching in agraph is a set of edges such that every vertex except oneis incident with exactly one edge in this set,and theexceptional vertex is incident to none.The matchingpreclusion number of a graph G,denoted ...  (本文共10页) 阅读全文>>