共查询到17条相似文献,搜索用时 78 毫秒
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六角系统是2-连通的平面图,其每个内部面都是单位正六边形.六角系统的完美匹配是化学中苯类芳烃体系的Kekule结构.一个六角系统H完美匹配Z—变换图Z(H)是一个图,它的顶点集是H的完匹配集,两个匹配相邻当且仅当它们的对称差是一个单位正六边形.本文用乘积图刻划了沙位六角系统Z—变换图的结构. 相似文献
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为了研究具有完美匹配图的Tuttc集和极端集,文献[1,2]提出了一种新的图运算,并且得到了许多有趣的性质。本文中,我们刻画了level(G)=0的具有唯一完美匹配的饱和图G,并且确定了具有唯一完美匹配图的D-图的边数的紧上界。 相似文献
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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. 相似文献
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完美匹配树的次大和次小的最大特征值 总被引:2,自引:0,他引:2
常安 《高校应用数学学报(A辑)》1999,14(4):397-403
本文讨论完美匹配树的次大和次小的最大特征值问题,得到了次大的最大特征值的上界的明确表达式并确定了达到此上界的极树,同时也得到了次小的最大特征值的下界并确定了相应的极树。 相似文献
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我们推导出两类四角系统的Wiener数和Hyper-Wiener数的计算公式. 相似文献
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目前我们已知的极大导出匹配可扩图只有Kn,n和K2n.为了研究它们是否是仅有的极大导出匹配可扩图,我们考虑了匹配数,导出匹配数,极大导出匹配可扩图以及一个相关的猜想,并得出了若干相关的结果. 相似文献
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Some Ore-type Results for Matching and Perfect Matching in <Emphasis Type="Italic">k</Emphasis>-uniform Hypergraphs
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Let S1 and S2 be two (k-1)-subsets in a k-uniform hypergraph H. We call S1 and S2 strongly or middle or weakly independent if H does not contain an edge e ∈ E(H) such that S1 ∩ e ≠∅ and S2 ∩ e ≠∅ or e ⊆ S1 ∪ S2 or e ⊇ S1 ∪ S2, respectively. In this paper, we obtain the following results concerning these three independence. (1) For any n ≥ 2k2-k and k ≥ 3, there exists an n-vertex k-uniform hypergraph, which has degree sum of any two strongly independent (k-1)-sets equal to 2n-4(k-1), contains no perfect matching; (2) Let d ≥ 1 be an integer and H be a k-uniform hypergraph of order n ≥ kd+(k-2)k. If the degree sum of any two middle independent (k-1)-subsets is larger than 2(d-1), then H contains a d-matching; (3) For all k ≥ 3 and sufficiently large n divisible by k, we completely determine the minimum degree sum of two weakly independent (k-1)-subsets that ensures a perfect matching in a k-uniform hypergraph H of order n. 相似文献
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Stephen G. Hartke Derrick Stolee Douglas B. West Matthew Yancey 《Journal of Graph Theory》2013,73(4):449-468
Let denote the maximum number of edges in a graph having n vertices and exactly p perfect matchings. For fixed p, Dudek and Schmitt showed that for some constant when n is at least some constant . For , they also determined and . For fixed p, we show that the extremal graphs for all n are determined by those with vertices. As a corollary, a computer search determines and for . We also present lower bounds on proving that for (as conjectured by Dudek and Schmitt), and we conjecture an upper bound on . Our structural results are based on Lovász's Cathedral Theorem. 相似文献
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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。 相似文献
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Let G be a 5‐connected triangulation of a surface Σ different from the sphere, and let be the Euler characteristic of Σ. Suppose that with even and M and N are two matchings in of sizes m and n respectively such that . It is shown that if the pairwise distance between any two elements of is at least five and the face‐width of the embedding of G in Σ is at least , then there is a perfect matching M0 in containing M such that . 相似文献
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多边形链图的完美匹配数(即多边形碳氢链状聚合物的Kekule结构数)是数学化学研究的重要内容之一。我们给出了一个求该数的简洁算法,并证明该数是一个多项式。做为应用,对于一类特殊的多边形链图,给出了具体的表达式。 相似文献