共查询到20条相似文献,搜索用时 15 毫秒
1.
A cubical polytope is a convex polytope all of whose facets are conbinatorial cubes. A d-polytope Pis called almost simple if, in the graph of P, each vertex of Pis d-valent of (d+ 1)-valent. It is known that, for d> 4, all but one cubical d-polytopes with up to 2d+1vertices are almost simple, which provides a complete enumeration of all the cubical d-polytopes with up to 2d+1vertices. We show that this result is also true for d=4. 相似文献
2.
In this note, we show that a nondegenerated polytope in IR
n
with n + k, 1 k < n, vertices is far from any symmetric body. We provide the asymptotically sharp estimates for the asymmetry constant of such polytopes. 相似文献
3.
An invariant σ2(G) of a graph is defined as follows: σ2(G) := min{d(u) + d(v)|u, v ∈V(G),uv ∈ E(G),u ≠ v} is the minimum degree sum of nonadjacent vertices (when G is a complete graph, we define σ2(G) = ∞). Let k, s be integers with k ≥ 2 and s ≥ 4, G be a graph of order n sufficiently large compared with s and k. We show that if σ2(G) ≥ n + k- 1, then for any set of k independent vertices v1,..., vk, G has k vertex-disjoint cycles C1,..., Ck such that |Ci| ≤ s and vi ∈ V(Ci) for all 1 ≤ i ≤ k.
The condition of degree sum σs(G) ≥ n + k - 1 is sharp. 相似文献
The condition of degree sum σs(G) ≥ n + k - 1 is sharp. 相似文献
4.
Rosa Antolini 《Applied Categorical Structures》2002,10(5):481-494
We investigate the category of cubical sets with some additional degeneracies called connections. We prove that the realisation of a cubical set with connections is independent, up to homotopy, of whether we collapse those extra degeneracies or not and that any cubical set which is Kan admits connections. Using this type of cubical sets we define the cubical classifying space of a category and prove that this is equivalent to the simplicial one. 相似文献
5.
In this paper, we prove that an m-connected graph G on n vertices has a spanning tree with at most k leaves (for k ≥ 2 and m ≥ 1) if every independent set of G with cardinality m + k contains at least one pair of vertices with degree sum at least n − k + 1. This is a common generalization of results due to Broersma and Tuinstra and to Win. 相似文献
6.
Zhi‐Hong Chen 《Journal of Graph Theory》2017,86(2):193-212
For a graph H , let for every edge . For and , let be a set of k‐edge‐connected K3‐free graphs of order at most r and without spanning closed trails. We show that for given and ε, if H is a k‐connected claw‐free graph of order n with and , and if n is sufficiently large, then either H is Hamiltonian or the Ryjác?ek's closure where G is an essentially k‐edge‐connected K3‐free graph that can be contracted to a graph in . As applications, we prove:
- (i) For , if and if and n is sufficiently large, then H is Hamiltonian.
- (ii) For , if and n is sufficiently large, then H is Hamiltonian.
7.
For a graph G, we define σ2(G) := min{d(u) + d(v)|u, v ≠ ∈ E(G), u ≠ v}. Let k ≥ 1 be an integer and G be a graph of order n ≥ 3k. We prove if σ2(G) ≥ n + k − 1, then for any set of k independent vertices v
1,...,v
k
, G has k vertex-disjoint cycles C
1,..., C
k
of length at most four such that v
i
∈ V(C
i
) for all 1 ≤ i ≤ k. And show if σ2(G) ≥ n + k − 1, then for any set of k independent vertices v
1,...,v
k
, G has k vertex-disjoint cycles C
1,..., C
k
such that v
i
∈ V(C
i
) for all 1 ≤ i ≤ k, V(C
1) ∪...∪ V(C
k
) = V(G), and |C
i
| ≤ 4 for all 1 ≤ i ≤ k − 1.
The condition of degree sum σ2(G) ≥ n + k − 1 is sharp.
Received: December 20, 2006. Final version received: December 12, 2007. 相似文献
8.
The modified method of refined bounds is proposed and experimentally studied. This method is designed to iteratively approximate convex multidimensional polytopes with a large number of vertices. Approximation is realized by a sequence of convex polytopes with a relatively small but gradually increasing number of vertices. The results of an experimental comparison between the modified and the original methods of refined bounds are presented. The latter was designed for the polyhedral approximation of multidimensional convex compact bodies of general type. 相似文献
9.
10.
Let K be a smooth convex set. The convex hull of independent random points in K is a random polytope. Central limit theorems for the volume and the number of i dimensional faces of random polytopes are proved as the number of random points tends to infinity. One essential step is
to determine the precise asymptotic order of the occurring variances.
Research was supported in part by the European Network PHD, MCRN-511953. 相似文献
11.
Daniel S. Farley 《Geometriae Dedicata》2005,110(1):221-242
A class of groups, called picture groups, is defined. Richard Thompsons groups F, T, and V are all picture groups. Each picture group is shown to act properly and isometrically on a CAT(0) cubical complex. In particular, all picture groups are a-T-menable.Mathematics Subject Classifications (2000). 20F65, 43A15. 相似文献
12.
The eccentricity of a vertex v in a graph is the maximum of the distances from v to all other vertices. The diameter of a graph is the maximum of the eccentricities of its vertices. Fix the parameters n, d, c. Over all graphs with order n and diameter d, we determine the maximum (within 1) and the minimum of the number of vertices with eccentricity c.
Revised: May 7, 1999 相似文献
13.
一个六点七边图的填充与覆盖 总被引:2,自引:1,他引:1
$\lambda{K_v}$为$\lambda$重$v$点完全图, $G$ 为有限简单图. $\lambda {K_v}$ 的一个 $G$-设计 ( $G$-填充设计, $G$-覆盖设计), 记为 ($v,G,\lambda$)-$GD$(($v,G,\lambda$)-$PD$, ($v,G,\lambda$)-$CD$), 是指一个序偶($X,\calB$),其中 $X$ 为 ${K_v}$ 的顶点集, $\cal B$ 为 ${K_v}$ 中同构于 $G$的子图的集合, 称为区组集,使得 ${K_v 相似文献
14.
15.
In this paper,we determine the unique graph with the largest signless Laplacian spectral radius among all the tricyclic graphs with n vertices and k pendant vertices. 相似文献
16.
Jia-zu ZHOU School of Mathematics Statistics Southwest University Chongqing China Department of Mathematics Polytechnic University Brooklyn NY USA 《中国科学A辑(英文版)》2007,50(3)
Let∑be a convex hypersurface in the Euclidean space R4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional∫∑H2dσ. This bound is an invariant involving the area of∑, the volume and Minkowski quermassintegrals of the convex body that∑bounds. We also obtain a sufficient condition for a convex body to contain another in the Euclidean space R4. 相似文献
17.
林跃峰 《数学的实践与认识》2013,43(10)
研究次极大图(即链环分支数等于基圈数的连通平图)的唯一性.证明了无割点且包含子图K_4的连通平图G是次极大图当且仅当G同构于K_4,并刻画了包含子图K_4的次极大图的结构. 相似文献
18.
Martins' algorithm revisited for multi-objective shortest path problems with a MaxMin cost function 总被引:1,自引:0,他引:1
Xavier Gandibleux Frédéric Beugnies Sabine Randriamasy 《4OR: A Quarterly Journal of Operations Research》2006,4(1):47-59
This paper presents a direct extension of the label setting algorithm proposed by Martins in 1984 for the shortest path problem
with multiple objectives. This extended version computes all the efficient paths from a given source vertex, to all the other
vertices of the network. The algorithm copes with problems in which the "cost values" associated with the network arcs are
positive. The proposed extension can handle objective functions that are either of the "sum" type or of the "bottleneck" type.
The main modifications to Martins' algorithm for multi-objective shortest path problems are linked to the dominance test and
the procedure for identifying efficient paths. The algorithmic features are described and a didactic example is provided to
illustrate the working principle. The results of numerical experiments concerning the number of efficient solutions produced
and the CPU time consumed for several configurations of objectives, on a set of randomly generated networks, are also provided.
Received: February 2005 / Revised version: June 2005
AMS classification:
90C29, 90C27, 05C38, 90B18, 68M12 相似文献
19.
XinghuaWang ChongLi 《计算数学(英文版)》2003,21(2):195-200
The convergence problem of the family of Euler-Halley methods is considered under the Lipschitz condition with the L-average,and a united convergence theory with its applications is presented. 相似文献
20.
Ruijuan Zhao Bing Zheng Maolin Liang Yangyang Xu 《Numerical Linear Algebra with Applications》2020,27(3)
This paper is concerned with computing ‐eigenpairs of symmetric tensors. We first show that computing ‐eigenpairs of a symmetric tensor is equivalent to finding the nonzero solutions of a nonlinear system of equations, and then propose a modified normalized Newton method (MNNM) for it. Our proposed MNNM method is proved to be locally and cubically convergent under some suitable conditions, which greatly improves the Newton correction method and the orthogonal Newton correction method recently provided by Jaffe, Weiss and Nadler since these two methods only enjoy a quadratic rate of convergence. As an application, the unitary symmetric eigenpairs of a complex‐valued symmetric tensor arising from the computation of quantum entanglement in quantum physics are calculated by the MNNM method. Some numerical results are presented to illustrate the efficiency and effectiveness of our method. 相似文献