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31.
Let p?1 and q?0 be integers. A family of sets F is (p,q)-intersecting when every subfamily FF formed by p or less members has total intersection of cardinality at least q. A family of sets F is (p,q)-Helly when every (p,q)-intersecting subfamily FF has total intersection of cardinality at least q. A graph G is a (p,q)-clique-Helly graph when its family of (maximal) cliques is (p,q)-Helly. According to this terminology, the usual Helly property and the clique-Helly graphs correspond to the case p=2,q=1. In this work we present a characterization for (p,q)-clique-Helly graphs. For fixed p,q, this characterization leads to a polynomial-time recognition algorithm. When p or q is not fixed, it is shown that the recognition of (p,q)-clique-Helly graphs is NP-hard.  相似文献   
32.
For a finite simple graph G, we denote the set of degrees of its vertices, known as its degree set, by D(G). Kapoor, Polimeni and Wall [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] have determined the least number of vertices among graphs with a given degree set. We give a very short proof of this result.  相似文献   
33.
We study the Helmholtz equation in the exterior of an infinite perturbed cylinder with a Dirichlet boundary condition. Existence and uniqueness of solutions are established using the variational technique introduced (SIAM J. Math. Anal. 2005; 37 (2):598–618). We also provide stability estimates with explicit dependence of the constants in terms of the frequency and the perturbed cylinder thickness. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   
34.
We study the maximum stable set problem. For a given graph, we establish several transformations among feasible solutions of different formulations of Lovász's theta function. We propose reductions from feasible solutions corresponding to a graph to those corresponding to its induced subgraphs. We develop an efficient, polynomial-time algorithm to extract a maximum stable set in a perfect graph using the theta function. Our algorithm iteratively transforms an approximate solution of the semidefinite formulation of the theta function into an approximate solution of another formulation, which is then used to identify a vertex that belongs to a maximum stable set. The subgraph induced by that vertex and its neighbors is removed and the same procedure is repeated on successively smaller graphs. We establish that solving the theta problem up to an adaptively chosen, fairly rough accuracy suffices in order for the algorithm to work properly. Furthermore, our algorithm successfully employs a warm-start strategy to recompute the theta function on smaller subgraphs. Computational results demonstrate that our algorithm can efficiently extract maximum stable sets in comparable time it takes to solve the theta problem on the original graph to optimality. This work was supported in part by NSF through CAREER Grant DMI-0237415. Part of this work was performed while the first author was at the Department of Applied Mathematics and Statisticsat Stony Brook University, Stony Brook, NY, USA.  相似文献   
35.
36.
本文利用ασ仿紧子集的概念,给出了在正则空间条件下,仿紧空间在连续闭映射下的原象是仿紧空间的一个充分条件.这一结果,统一推广了高国士教授与陈必胜教授在两篇论文中的结果.  相似文献   
37.
本文讨论了笔者在[1]中提出的伪凸集,拟凸集的支撑函数与障碍锥的性质,并通过这些性质得出了二个闭性准则。  相似文献   
38.
Fuzzy集的基数   总被引:6,自引:0,他引:6  
关于Fuzzy集的基数,[1]中曾对有限支集的Fuzzy集以及极苛刻条件下的无限Fuzzy集给出过一种定义。但是,正如本文将要指出的那样,该定义是不合理的。本文将从研究Fuzzy映射入手,给出Fuzzy集基数的一般性定义。基于这一定义,不但得到有关基数的大部分结论,而且有其自身的特殊性。  相似文献   
39.
We give an estimate for the number of elements in the intersection of topological Sidon sets inR n with compact convex subsets and deduce a necessary and sufficient conditions for an orbit of a linear transformation ofR n to be a topological Sidon set.  相似文献   
40.
Fixed Point Theorems on Product Topological Spaces and Applications   总被引:3,自引:0,他引:3  
A new collectively fixed point theorem for a family of set-valued mappings defined on product spaces of non-compact topological spaces without linear structure is proved and some special cases are also discussed. As applications, some non-empty intersection theorems of sets with convex sections and equilibrium existence theorem of abstract economies are obtained under much weaker assumptions. Our results includes a number of known results as many special cases.  相似文献   
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