首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
A subspace bitrade of type Tq(t,k,v) is a pair (T0,T1) of two disjoint nonempty collections of k-dimensional subspaces of a v-dimensional space V over the finite field of order q such that every t-dimensional subspace of V is covered by the same number of subspaces from T0 and T1. In a previous paper, the minimum cardinality of a subspace Tq(t,t+1,v) bitrade was established. We generalize that result by showing that for admissible v, t, and k, the minimum cardinality of a subspace Tq(t,k,v) bitrade does not depend on k. An example of a minimum bitrade is represented using generator matrices in the reduced echelon form. For t=1, the uniqueness of a minimum bitrade is proved.  相似文献   

2.
3.
Let P1=v1,v2,v3,,vn and P2=u1,u2,u3,,un be two hamiltonian paths of G. We say that P1 and P2 are independent if u1=v1,un=vn, and uivi for 1<i<n. We say a set of hamiltonian paths P1,P2,,Ps of G between two distinct vertices are mutually independent if any two distinct paths in the set are independent. We use n to denote the number of vertices and use e to denote the number of edges in graph G. Moreover, we use ē to denote the number of edges in the complement of G. Suppose that G is a graph with ēn4 and n4. We prove that there are at least n2ē mutually independent hamiltonian paths between any pair of distinct vertices of G except n=5 and ē=1. Assume that G is a graph with the degree sum of any two non-adjacent vertices being at least n+2. Let u and v be any two distinct vertices of G. We prove that there are degG(u)+degG(v)n mutually independent hamiltonian paths between u and v if (u,v)E(G) and there are degG(u)+degG(v)n+2 mutually independent hamiltonian paths between u and v if otherwise.  相似文献   

4.
5.
6.
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 uL3, with ?uL3/2,, where L3, and L3/2, are the Lorentz spaces. Our criterion asserts that if u and v are the solutions, u is small in L3, and u,vLp for some p>3, then u=v. The proof is based on analysis of the dual equation with the aid of the bootstrap argument.  相似文献   

7.
8.
9.
In this paper, we consider the following nonlinear Kirchhoff wave equation (1){utt???x(μ(x,t,u,6ux62)ux)=f(x,t,u,ux,ut),0<x<1,0<t<T,u(0,t)=g0(t),u(1,t)=g1(t),u(x,0)=u?0(x),ut(x,0)=u?1(x), where u?0, u?1, μ, f, g0, g1 are given functions and 6ux62=01ux2(x,t)dx. 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 μ(x,t,y,z) around the point (x,t,y0,z0) up to order N+1, we establish an asymptotic expansion of high order in many small parameters of solution.  相似文献   

10.
For bipartite graphs G1,G2,,Gk, the bipartite Ramsey number b(G1,G2,,Gk) is the least positive integer b so that any coloring of the edges of Kb,b with k colors will result in a copy of Gi in the ith color for some i. In this paper, our main focus will be to bound the following numbers: b(C2t1,C2t2) and b(C2t1,C2t2,C2t3) for all ti3,b(C2t1,C2t2,C2t3,C2t4) for 3ti9, and b(C2t1,C2t2,C2t3,C2t4,C2t5) for 3ti5. 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   

11.
In this paper we consider the following competitive two-species chemotaxis system with two chemicals ut=Δuχ1(uv)+μ1u(1ua1w),xΩ,t>0,0=Δvv+w,xΩ,t>0,wt=Δwχ2(wz)+μ2w(1a2uw),xΩ,t>0,0=Δzz+u,xΩ,t>0in a smooth bounded domain ΩRn with n1, where χi0, ai0 and μi>0 (i=1,2). For the case a1>1>a20, it will be proved that if χ1χ2<μ1μ2, χ1a1μ1 and χ2<μ2, then the initial–boundary value problem with homogeneous Neumann boundary condition admits a unique global bounded solution and (u,v,w,z)(0,1,1,0) uniformly on Ω̄ as t.  相似文献   

12.
13.
14.
15.
16.
17.
18.
Xiuyun Wang 《Discrete Mathematics》2017,340(12):3016-3019
The double generalized Petersen graph DP(n,t), n3 and tZn?{0}, 22t<n, has vertex-set {xi,yi,ui,viiZn}, edge-set {{xi,xi+1},{yi,yi+1},{ui,vi+t},{vi,ui+t},{xi,ui},{yi,vi}iZn}. 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 DP(n,t), and conjectured that all DP(n,t) are Hamiltonian. In this paper, we prove this conjecture.  相似文献   

19.
For a graph H, let σt(H)=min{Σi=1tdH(vi)|{v1,v2,,vt}is an independent set in H} and let Ut(H)=min{|?i=1tNH(vi)||{v1,v2,?,vt}is an independent set in H}. We show that for a given number ? and given integers pt>0, k{2,3} and N=N(p,?), if H is a k-connected claw-free graph of order n>N with δ(H)3 and its Ryjác?ek’s closure cl(H)=L(G), and if dt(H)t(n+?)p where dt(H){σt(H),Ut(H)}, then either H is Hamiltonian or G, the preimage of L(G), can be contracted to a k-edge-connected K3-free graph of order at most max{4p?5,2p+1} and without spanning closed trails. As applications, we prove the following for such graphs H of order n with n sufficiently large:(i) If k=2, δ(H)3, and for a given t (1t4) dt(H)tn4, then either H is Hamiltonian or cl(H)=L(G) where G is a graph obtained from K2,3 by replacing each of the degree 2 vertices by a K1,s (s1). When t=4 and dt(H)=σ4(H), this proves a conjecture in Frydrych (2001).(ii) If k=3, δ(H)24, and for a given t (1t10) dt(H)>t(n+5)10, then H is Hamiltonian. These bounds on dt(H) in (i) and (ii) are sharp. It unifies and improves several prior results on conditions involved σt and Ut for the hamiltonicity of claw-free graphs. Since the number of graphs of orders at most max{4p?5,2p+1} are fixed for given p, improvements to (i) or (ii) by increasing the value of p are possible with the help of a computer.  相似文献   

20.
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号