共查询到20条相似文献,搜索用时 15 毫秒
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Denis S. Krotov 《Discrete Mathematics》2017,340(12):2723-2731
A subspace bitrade of type is a pair of two disjoint nonempty collections of -dimensional subspaces of a -dimensional space over the finite field of order such that every -dimensional subspace of is covered by the same number of subspaces from and . In a previous paper, the minimum cardinality of a subspace bitrade was established. We generalize that result by showing that for admissible , , and , the minimum cardinality of a subspace bitrade does not depend on . An example of a minimum bitrade is represented using generator matrices in the reduced echelon form. For , the uniqueness of a minimum bitrade is proved. 相似文献
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《Applied Mathematics Letters》2006,19(4):345-350
Let and be two hamiltonian paths of . We say that and are independent if , and for . We say a set of hamiltonian paths of between two distinct vertices are mutually independent if any two distinct paths in the set are independent. We use to denote the number of vertices and use to denote the number of edges in graph . Moreover, we use to denote the number of edges in the complement of . Suppose that is a graph with and . We prove that there are at least mutually independent hamiltonian paths between any pair of distinct vertices of except and . Assume that is a graph with the degree sum of any two non-adjacent vertices being at least . Let and be any two distinct vertices of . We prove that there are mutually independent hamiltonian paths between and if and there are mutually independent hamiltonian paths between and if otherwise. 相似文献
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Tomoyuki Nakatsuka 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(8):3457-3464
The aim of this paper is to prove a uniqueness criterion for solutions to the stationary Navier–Stokes equation in 3-dimensional exterior domains within the class with , where and are the Lorentz spaces. Our criterion asserts that if and are the solutions, is small in and for some , then . The proof is based on analysis of the dual equation with the aid of the bootstrap argument. 相似文献
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Le Thi Phuong Ngoc Nguyen Anh Triet Nguyen Thanh Long 《Nonlinear Analysis: Real World Applications》2010,11(4):2479-2501
In this paper, we consider the following nonlinear Kirchhoff wave equation (1) where , , , , , are given functions and . First, combining the linearization method for nonlinear term, the Faedo–Galerkin method and the weak compact method, a unique weak solution of problem (1) is obtained. Next, by using Taylor’s expansion of the function around the point up to order , we establish an asymptotic expansion of high order in many small parameters of solution. 相似文献
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For bipartite graphs , the bipartite Ramsey number is the least positive integer so that any coloring of the edges of with colors will result in a copy of in the th color for some . In this paper, our main focus will be to bound the following numbers: and for all for and for Furthermore, we will also show that these mentioned bounds are generally better than the bounds obtained by using the best known Zarankiewicz-type result. 相似文献
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In this paper we consider the following competitive two-species chemotaxis system with two chemicals in a smooth bounded domain with , where , and . For the case , it will be proved that if , and , then the initial–boundary value problem with homogeneous Neumann boundary condition admits a unique global bounded solution and uniformly on as . 相似文献
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Xiuyun Wang 《Discrete Mathematics》2017,340(12):3016-3019
The double generalized Petersen graph , and , , has vertex-set , edge-set . These graphs were first defined by Zhou and Feng as examples of vertex-transitive non-Cayley graphs. Then, Kutnar and Petecki considered the structural properties, Hamiltonicity properties, vertex-coloring and edge-coloring of , and conjectured that all are Hamiltonian. In this paper, we prove this conjecture. 相似文献
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Zhi-Hong Chen 《Discrete Mathematics》2017,340(12):3104-3115
For a graph , let and let . We show that for a given number and given integers , and , if is a -connected claw-free graph of order with and its Ryjác?ek’s closure , and if where , then either is Hamiltonian or , the preimage of , can be contracted to a -edge-connected -free graph of order at most and without spanning closed trails. As applications, we prove the following for such graphs of order with sufficiently large:(i) If , , and for a given () , then either is Hamiltonian or where is a graph obtained from by replacing each of the degree 2 vertices by a (). When and , this proves a conjecture in Frydrych (2001).(ii) If , , and for a given () , then is Hamiltonian. These bounds on in (i) and (ii) are sharp. It unifies and improves several prior results on conditions involved and for the hamiltonicity of claw-free graphs. Since the number of graphs of orders at most are fixed for given , improvements to (i) or (ii) by increasing the value of are possible with the help of a computer. 相似文献