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1.
关于图的一种新分解   总被引:2,自引:1,他引:1  
马克杰  陈怀堂 《数学进展》1991,20(2):240-246
一、概念和记号 最近,Yousef Alavi等人在文献[*]中给出了图的升分解概念:已知图G,存在自然数n,G的边数q满足( )≤q≤( )。如果G能分解为子图G_1,G_2,…,G_n的并,使得G_i与G_(i+1)的一个真子图同构(1≤i≤n=1),G_i不含孤立点,则称这个分解为图G的一个升分解。  相似文献   

2.
Let m, n, S_1, S_2, …, S_n, be non-negative integers with 0≤m≤n. Assume μ(S_1, S_2, …, S_n)={(a_1, a_2, …, a_n)|0≤a_i≤S_i for each i} is a poser, Where (a_1, a_2, …, a_n)<(b_1, b_2, …, b_n) if and only if a_i相似文献   

3.
关于图升分解为独立边集问题   总被引:1,自引:0,他引:1  
Alavi[1]给出了图的升分解概念,并猜想每一图都可升分解.本文证明了边数为(?)的图G当边色数X'(G)≤(n+2)/2时可升分解为{Gi}, 1≤i≤n, Gi≈iK2.  相似文献   

4.
图中具有正交(g,f)因子分解的子图   总被引:1,自引:0,他引:1  
设G是一个 (mg +k ,mf -k) -图 (1≤k 相似文献   

5.
关于图的升分解问题   总被引:3,自引:0,他引:3  
1987年,文献[1]中给出了图的升分解概念.已知图 G 和自然数 n,G 的边数 q 满足(?)≤q<(?).如果 G 能分解为子图 G_1,G_2,…,G_n 的并,满足 G_i 与G_(i+1)的一个真子图同构(1≤i≤n-1),G_i 不含孤立点,则称这个分解为图 G 的一个升分解.  相似文献   

6.
设 F(n,k)为由1,2,…,n 组成的数列 S_(n,k)的最小长度,S_(n,k)满足对每个自然数 i≤k,它的前 F(n,i)项含1,2…,n 的全部 i-排列.本文证明,F(n,k)≤k(n-1)+1-[(K+2)/6]-[K/6]-[(K-2/6)]并猜想,这是最好结果.  相似文献   

7.
设G是一个顶点集为V(G),边集为E(G))的简单图.S_k(G)表示图G的拉普拉斯特征值的前k项部分和.Brouwer et al.给出如下猜想:S_k(G)≤e(G)+((k+1)/2),1≤k≤n.证明了当k=3时,对边数不少于n~2/4-n/4的图及有完美匹配或有6-匹配的图,猜想是正确的.  相似文献   

8.
设G=(X,Y,E(G))是一个二分图,分别用V(G)=XUY和E(G)表示G的顶点集和边集.设f是定义在V(G)上的整数值函数且对(A)x∈V(G)有f(x)≥k.设H_1,H_2,…,H_k是G的k个顶点不相交的子图,且|E(H_i)|=m,1≤i≤k.本文证明了每个二分(0,mf-m+1)-图G有一个(0,f)-因子分解正交于Hi(i=1,2,…,k).  相似文献   

9.
<正>在学习数学时,如统计、数列或微积分中经常遇到若干数(或单项式)相加的式子a_1+a_2+…+a_n,为了书写方便,常把上式记作n∑(i=1)a_i或∑(1≤i≤n)a_i,即a_1+a_2+…+a_n=n∑ (i=1)a_i=∑(1≤i≤n)a_i.上面式中的记号∑表示关于数连加求和,称为总和号,∑是一个大写的希腊字母,读作sigma,a_i表示一般项,i是整数,称为求和  相似文献   

10.
设k≥2,1≤a_1相似文献   

11.
If a graph G decomposes into edge‐disjoint 4‐cycles, then each vertex of G has even degree and 4 divides the number of edges in G. It is shown that these obvious necessary conditions are also sufficient when G is any simple graph having minimum degree at least , where n is the number of vertices in G. This improves the bound given by Gustavsson (PhD Thesis, University of Stockholm, 1991), who showed (as part of a more general result) sufficiency for simple graphs with minimum degree at least . On the other hand, it is known that for arbitrarily large values of n there exist simple graphs satisfying the obvious necessary conditions, having n vertices and minimum degree , but having no decomposition into edge‐disjoint 4‐cycles. We also show that if G is a bipartite simple graph with n vertices in each part, then the obvious necessary conditions for G to decompose into 4‐cycles are sufficient when G has minimum degree at least .  相似文献   

12.
Y.Alavi,P.Erds等人在[1]中提出猜想:设自然数α_1,α_2…α_k满足且,则可以划分成k个互不相交子集S_1,S_2,···,S_k,满足.本文证明了这个猜想。  相似文献   

13.
T∞-测度分解定理的进一步讨论   总被引:1,自引:0,他引:1  
在对T∞-测度做进一步研究的基础上,得到了(有限或无限)T∞-测度的Hahn分解定理和Jordan分解定理。同时,用一种新方法证明了有限T∞-测度的Lebesgue分解定理。此外,还得到了一些类似于经典测度的结论。  相似文献   

14.
An algorithm for computing the complete CS decomposition of a partitioned unitary matrix is developed. Although the existence of the CS decomposition (CSD) has been recognized since 1977, prior algorithms compute only a reduced version. This reduced version, which might be called a 2-by-1 CSD, is equivalent to two simultaneous singular value decompositions. The algorithm presented in this article computes the complete 2-by-2 CSD, which requires the simultaneous diagonalization of all four blocks of a unitary matrix partitioned into a 2-by-2 block structure. The algorithm appears to be the only fully specified algorithm available. The computation occurs in two phases. In the first phase, the unitary matrix is reduced to bidiagonal block form, as described by Sutton and Edelman. In the second phase, the blocks are simultaneously diagonalized using techniques from bidiagonal SVD algorithms of Golub, Kahan, Reinsch, and Demmel. The algorithm has a number of desirable numerical features.   相似文献   

15.
A Nash group is said to be almost linear if it has a Nash representation with a finite kernel. Structures and basic properties of these groups are studied.  相似文献   

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For an ordered k-decomposition of a connected graph G and an edge e of G, the -code of e is the k-tuple where d(e, G i) is the distance from e to G i. A decomposition is resolving if every two distinct edges of G have distinct -codes. The minimum k for which G has a resolving k-decomposition is its decomposition dimension dim d (G). A resolving decomposition of G is connected if each G i is connected for 1 i k. The minimum k for which G has a connected resolving k-decomposition is its connected decomposition number cd(G). Thus 2 dim d (G) cd(G) m for every connected graph G of size m 2. All nontrivial connected graphs of size m with connected decomposition number 2 or m have been characterized. We present characterizations for connected graphs of size m with connected decomposition number m – 1 or m – 2. It is shown that each pair s, t of rational numbers with 0 < s t 1, there is a connected graph G of size m such that dim d (G)/m = s and cd(G)/m = t.  相似文献   

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We consider weighted anchored and ANOVA spaces of functions with first order mixed derivatives bounded in Lp. Recently, Hefter, Ritter and Wasilkowski established conditions on the weights in the cases p=1 and p= which ensure equivalence of the corresponding norms uniformly in the dimension or only polynomially dependent on the dimension. We extend these results to the whole range of p[1,]. It is shown how this can be achieved via interpolation.  相似文献   

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