共查询到20条相似文献,搜索用时 25 毫秒
1.
Teresa W. Haynes Michael A. Henning Lucas C. van der Merwe Anders Yeo 《Discrete Mathematics》2011,311(17):315
A graph G is diameter 2-critical if its diameter is two, and the deletion of any edge increases the diameter. Murty and Simon conjectured that the number of edges in a diameter 2-critical graph of order n is at most n2/4 and that the extremal graphs are complete bipartite graphs with equal size partite sets. We use an association with total domination to prove the conjecture for the graphs whose complements have diameter three. 相似文献
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WANG Tao&YU QingLin Institute of Applied Mathematics College of Mathematics Information Science Henan University Kaifeng China 《中国科学 数学(英文版)》2010,(5)
For a graph G =(V,E),a subset VS is a dominating set if every vertex in V is either in S or is adjacent to a vertex in S.The domination number γ(G) of G is the minimum order of a dominating set in G.A graph G is said to be domination vertex critical,if γ(G-v) γ(G) for any vertex v in G.A graph G is domination edge critical,if γ(G ∪ e) γ(G) for any edge e ∈/E(G).We call a graph G k-γ-vertex-critical(resp.k-γ-edge-critical) if it is domination vertex critical(resp.domination edge critical) and γ(G) = k.Ananchuen and Plummer posed the conjecture:Let G be a k-connected graph with the minimum degree at least k+1,where k 2 and k≡|V|(mod 2).If G is 3-γ-edge-critical and claw-free,then G is k-factor-critical.In this paper we present a proof to this conjecture,and we also discuss the properties such as connectivity and bicriticality in 3-γ-vertex-critical claw-free graph. 相似文献
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C. Pintea 《Proceedings of the American Mathematical Society》2000,128(11):3435-3444
In this paper we shall give some sufficient conditions in order that the so-called -category of a pair of differentiable manifolds be infinite.
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Ma Li 《偏微分方程(英文版)》1991,4(3)
In this paper, we study the following Eigen-problem {-\frac{∂}{∂x_i}(a_{ij}(x, u)\frac{∂u}{∂x_j}) + \frac{1}{2}a_{iju}(x,u)\frac{∂u}{∂x_i}\frac{∂u}{∂x_j} + h(x)u = μμ\frac{n+2}{n-2} \quad in Ω \qquad (0.1) u = 0 \quad on ∂Ω u > 0 \quad in Ω ⊂ R^n under some assumptions. First. we minimize I(u) = \frac{1}{2}∫_Ωa_{ij}(x, u)\frac{∂u}{∂x_i}\frac{∂u}{∂x_j} + h(x)u² over E_α = {u ∈ H¹_0(Ω); ∫_Ωu^α = 1} ( 2 < α < N = \frac{2n}{n-2}) to give a H¹_0-solution U_α of the perturbation problems of (0.1). Since I is not differentiable in H¹_0(Ω), the key point is the estimate of U_α. Then, we derive local uniform bounds of (U_α) and give a 'bad' solution of (0.1). Last, we remove the singular points of the 'bad' solution to obtain a solution of (0.1), our result is a extension of that of Brezis & Nirenberg. 相似文献
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Results of Lovász (1972) and Padberg (1974) imply that partitionable graphs contain all the potential counterexamples to Berge's famous Strong Perfect Graph Conjecture. A recursive method of generating partitionable graphs was suggested by Chvátal, Graham, Perold, and Whitesides (1979). Results of Seb? (1996) entail that Berge's conjecture holds for all the partitionable graphs obtained by this method. Here we suggest a more general recursion. Computer experiments show that it generates all the partitionable graphs with ω=3,α ≤ 9 (and we conjecture that the same will hold for bigger α, too) and many but not all for (ω,α)=(4,4) and (4,5). Here, α and ω are respectively the clique and stability numbers of a partitionable graph, that is the numbers of vertices in its maximum cliques and stable sets. All the partitionable graphs generated by our method contain a critical ω‐clique, that is an ω‐clique which intersects only 2ω?2 other ω‐cliques. This property might imply that in our class there are no counterexamples to Berge's conjecture (cf. Seb? (1996)), however this question is still open. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 259–285, 2002 相似文献
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It is often said that the Morse-Bott Lemma can be viewed as a “parameterized” Morse Lemma, and its proof should follow from the differentiability of the methods used to prove the Morse Lemma. The goal of this expository paper is to fill in the details. We present Palais' proof of the Morse Lemma using Moser's path method, which yields the necessary differentiability. 相似文献
9.
The buckling in stability of a long multilayer linearly viscoelastic shell, composed of different materials and loaded with
a uniformly distributed external pressure of given intensity, is investigated. By neglecting the influence of fastening of
its end faces, the initial problem is reduced to an analysis of the loss of load-carrying capacity of a ring of unit width
separated from the shell. The new problem is solved by using a mixed-type variational method, allowing for the geometric nonlinearity,
together with the Rayleigh-Ritz method. The creep kernels are taken exponential with equal indices of creep. As an example,
a three-layer ring with a structure symmetric about its midsurface is considered, and the effect of its physicomechanical
and geometrical parameters, as well as of wave formation, on the critical time of buckling in stability of the ring is determined.
It is found that, by selecting appropriate materials, more efficient multilayer shell-type structural members can be created.
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Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 617–628, September–October, 2007. 相似文献
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David Cariolaro 《Journal of Graph Theory》2006,51(4):301-318
We introduce a unifying framework for studying edge‐coloring problems on multigraphs. This is defined in terms of a rooted directed multigraph , which is naturally associated to the set of fans based at a given vertex u in a multigraph G. We call the “Fan Digraph.” We show that fans in G based at u are in one‐to‐one correspondence with directed trails in starting at the root of . We state and prove a central theorem about the fan digraph, which embodies many edge‐coloring results and expresses them at a higher level of abstraction. Using this result, we derive short proofs of classical theorems. We conclude with a new, generalized version of Vizing's Adjacency Lemma for multigraphs, which is stronger than all those known to the author. © 2005 Wiley Periodicals, Inc. J Graph Theory 51: 301–318, 2006 相似文献
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This paper deals with the Cauchy problem to the nonlinear pseudo-parabolic system ut-△u-αut=vp,vt-△v-αvt=uqwith p,q 1 and pq1,where the viscous terms of third order are included.We first find the critical Fujita exponent,and then determine the second critical exponent to characterize the critical space-decay rate of initial data in the co-existence region of global and non-global solutions.Moreover,time-decay profiles are obtained for the global solutions.It can be found that,diferent from those for the situations of general semilinear heat systems,we have to use distinctive techniques to treat the influence from the viscous terms of the highest order.To fix the non-global solutions,we exploit the test function method,instead of the general Kaplan method for heat systems.To obtain the global solutions,we apply the Lp-Lq technique to establish some uniform Lmtime-decay estimates.In particular,under a suitable classification for the nonlinear parameters and the initial data,various Lmtime-decay estimates in the procedure enable us to arrive at the time-decay profiles of solutions to the system.It is mentioned that the general scaling method for parabolic problems relies heavily on regularizing efect to establish the compactness of approximating solutions,which cannot be directly realized here due to absence of the smooth efect in the pseudo-parabolic system. 相似文献
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A. N. Vasil’ev 《Theoretical and Mathematical Physics》2007,153(1):1458-1462
We analyze the features of solutions for pair correlation functions in the case of a multicomponent liquid. We obtain these
solutions based on the Ornstein-Zernike equation. In the anomalous-dimension approximation, we find expressions for pair correlation
functions in the case of a spatially unbounded multicomponent liquid. We show that all pair correlation functions for a system
in the close vicinity of the critical state are described by a general expression similar to the expression for a pair correlation
function in the case of a one-component liquid.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 124–129, October, 2007. 相似文献
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Frank Merle 《Journal of the American Mathematical Society》2001,14(3):555-578
For the critical generalized Korteweg-de Vries equation, we establish blow-up in finite or infinite time in for initial data with negative energy, close to a soliton up to scaling and translation.
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It is shown that each critical set in a Latin square of order n > 6 has to have at least empty cells. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 77–83, 2007 相似文献
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Let M be a compact, smooth, 2-connected, 2m-dimensional manifoldwith M simply connected. If M has the homotopytype of an m-dimensionalCW-complex, then it supports a smooth, self-indexed function,maximal, constant and regular on M with at most cat(M) + 2 criticalpoints, all of which are of a certain reasonabletype. To such a critical point there corresponds, homotopically,the attachment of a cone. Conversely, to a cone attachment wemay associate, under certain dimensionality and connectivityconditions, a reasonable critical point. 1991Mathematics Subject Classification: primary 55M30, 57R70; secondary58E05, 55P50, 55P62. 相似文献
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Derényi, Palla and Vicsek introduced the following dependent percolation model, in the context of finding communities in networks. Starting with a random graph Ggenerated by some rule, form an auxiliary graph G′ whose vertices are the k‐cliques of G, in which two vertices are joined if the corresponding cliques share k – 1 vertices. They considered in particular the case where G = G(n,p), and found heuristically the threshold function p = p(n) above which a giant component appears in G′. Here we give a rigorous proof of this result, as well as many extensions. The model turns out to be very interesting due to the essential global dependence present in G′. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009 相似文献
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A graph is a k‐critical graph if G is not ‐colorable but every proper subgraph of G is ‐colorable. In this article, we construct a family of 4‐critical planar graphs with n vertices and edges. As a consequence, this improves the bound for the maximum edge density attained by Abbott and Zhou. We conjecture that this is the largest edge density for a 4‐critical planar graph. 相似文献