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A graph is called supereulerian if it has a spanning closed trail. Let G be a 2-edge-connected graph of order n such that each minimal edge cut SE(G) with |S|3 satisfies the property that each component of G−S has order at least (n−2)/5. We prove that either G is supereulerian or G belongs to one of two classes of exceptional graphs. Our results slightly improve earlier results of Catlin and Li. Furthermore, our main result implies the following strengthening of a theorem of Lai within the class of graphs with minimum degree δ4: If G is a 2-edge-connected graph of order n with δ(G)4 such that for every edge xyE(G) , we have max{d(x),d(y)}(n−2)/5−1, then either G is supereulerian or G belongs to one of two classes of exceptional graphs. We show that the condition δ(G)4 cannot be relaxed. 相似文献
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Mihran Papikian 《Transactions of the American Mathematical Society》2007,359(7):3483-3503
Under a certain assumption, similar to Manin's conjecture, we prove an upper bound on the degree of modular parametrizations of elliptic curves by Drinfeld modular curves, which is the function field analogue of the conjectured bound over the rational numbers.
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设σ(k,n)表示最小的正整数m,使得对于每个n项正可图序列,当其项和至少为m时,有一个实现含k 1个顶点的团作为其子图。Erdos等人猜想:σ(k,n)=(k-1)(2n-k) 2.Li等人证明了这个猜想对于k≥5,n≥(^k2))+3是对的,并且提出如下问题:确定最小的整数N(k),使得这个猜想对于n≥N(k)成立。他们同时指出:当k≥5时,[5k-1/2]≤N(k)≤(^k2) 3.Mubayi猜想:当k≥5时,N(k)=[5k-1/2]。在本文中,我们证明了N(8)=20,即Mubayi猜想对于k=8是成立的。 相似文献
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Amitabha Tripathi 《Discrete Applied Mathematics》2007,155(5):670-671
For a finite simple graph G, we denote the set of degrees of its vertices, known as its degree set, by D(G). Kapoor, Polimeni and Wall [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] have determined the least number of vertices among graphs with a given degree set. We give a very short proof of this result. 相似文献
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Maurits de Graaf 《Discrete Mathematics》2004,280(1-3):219-223
We show that each directed graph (with no parallel arcs) on n vertices, each with indegree and outdegree at least n/twhere t=2.888997… contains a directed circuit of length at most 3. 相似文献
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A class of long-range predictive adaptive fuzzy relational controllers is presented. The plant behavior is described over an extended time horizon by a fuzzy relational model which is identified based on input-output closed-loop observations of the plant variables. In this class of adaptive controllers the control law attempts to minimize a quadratic cost over an extended control horizon. When used with linear models, this approach has revealed a significant potential for overcoming the limitations of one-step ahead schemes, such as the stabilization of non-minimum phase plants. Here, a uniform framework is adopted for implementing both the fuzzy model and the fuzzy controller, namely distributed fuzzy relational structures gaining from their massive parallel processing features and from the learning capabilities typical of the connectivist approaches. Issues such as maintenance during the adaptation process of the meaning of linguistic terms used at both fuzzy systems interfaces are addressed, namely by introducing a new design methodology for on-line fuzzy systems interface adaptation. The examples presented reinforce the claim of the usefulness of this new approach. 相似文献
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D.C.隶属函数模糊集及其应用(Ⅱ)--D.C.隶属函数模糊集的万能逼近性 总被引:1,自引:0,他引:1
本文是D.C.隶属函数模糊集及其应用系列研究的第二部分。指出在实际问题中普遍选用的三角形、半三角形、梯形、半梯形、高斯型、柯西型、S形、Z形、π形隶属函数模糊集等均为D.C.隶属函数模糊集,建立了D.C.隶属函数模糊集对模糊集的万有逼近性。探讨了D.C.隶属函数模糊集与模糊数之间的关系,给出了用D.C.隶属函数模糊集逼近模糊数的e-Cellina逼近形式,得到模糊数与D.C.函数之间的一个对应算子,指出了用模糊数表示D.C.函数的问题。 相似文献