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11.
Volker Stix 《Computational Optimization and Applications》2004,27(2):173-186
Clustering applications dealing with perception based or biased data lead to models with non-disjunct clusters. There, objects to be clustered are allowed to belong to several clusters at the same time which results in a fuzzy clustering. It can be shown that this is equivalent to searching all maximal cliques in dynamic graphs like G
t = (V,E
t), where E
t – 1 E
t, t = 1,...,T; E
0 = . In this article algorithms are provided to track all maximal cliques in a fully dynamic graph. 相似文献
12.
JiongShengLI YongLiangPAN 《数学学报(英文版)》2004,20(5):803-806
We first apply non-negative matrix theory to the matrix K = D A, where D and A are the degree-diagonal and adjacency matrices of a graph G, respectively, to establish a relation on the largest Laplacian eigenvalue λ1 (G) of G and the spectral radius p(K) of K. And then by using this relation we present two upper bounds for λ1(G) and determine the extremal graphs which achieve the upper bounds. 相似文献
13.
Simple ingredients leading to very efficient heuristics for the maximum clique problem 总被引:2,自引:0,他引:2
Starting from an algorithm recently proposed by Pullan and Hoos, we formulate and analyze iterated local search algorithms
for the maximum clique problem. The basic components of such algorithms are a fast neighbourhood search (not based on node
evaluation but on completely random selection) and simple, yet very effective, diversification techniques and restart rules.
A detailed computational study is performed in order to identify strengths and weaknesses of the proposed algorithms and the
role of the different components on several classes of instances. The tested algorithms are very fast and reliable: most of
the DIMACS benchmark instances are solved within very short CPU times. For one of the hardest tests, a new putative optimum
was discovered by one of our algorithms. Very good performances were also shown on recently proposed and more difficult instances.
It is important to remark that the heuristics tested in this paper are basically parameter free (the appropriate value for
the unique parameter is easily identified and was, in fact, the same value for all problem instances used in this paper). 相似文献
14.
Pablo De Caria 《Journal of Graph Theory》2014,77(1):39-57
Let be the class of all graphs and K be the clique operator. The validity of the equality has been an open question for several years. A graph in but not in is exhibited here. 相似文献
15.
Yoshio Sano 《Discrete Applied Mathematics》2009,157(13):2978-2982
The notion of a competition multigraph was introduced by C. A. Anderson, K. F. Jones, J. R. Lundgren, and T. A. McKee [C. A. Anderson, K. F. Jones, J. R. Lundgren, and T. A. McKee: Competition multigraphs and the multicompetition number, Ars Combinatoria 29B (1990) 185-192] as a generalization of the competition graphs of digraphs.In this note, we give a characterization of competition multigraphs of arbitrary digraphs and a characterization of competition multigraphs of loopless digraphs. Moreover, we characterize multigraphs whose multicompetition numbers are at most m, where m is a given nonnegative integer and give characterizations of competition multihypergraphs. 相似文献
16.
David R. Wood 《Graphs and Combinatorics》2007,23(3):337-352
A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following
graph classes: (1) graphs with n vertices and m edges; (2) graphs with n vertices, m edges, and maximum degree Δ; (3) d-degenerate graphs with n vertices and m edges; (4) planar graphs with n vertices and m edges; and (5) graphs with n vertices and no K5-minor or no K3,3-minor. For example, the maximum number of cliques in a planar graph with n vertices is 8(n − 2).
Research supported by a Marie Curie Fellowship of the European Community under contract 023865, and by the projects MCYT-FEDER
BFM2003-00368 and Gen. Cat 2001SGR00224. 相似文献
17.
18.
The class of cographs is known to have unbounded linear clique‐width. We prove that a hereditary class of cographs has bounded linear clique‐width if and only if it does not contain all quasi‐threshold graphs or their complements. The proof borrows ideas from the enumeration of permutation classes. 相似文献
19.
Inspired by the “generalized t‐designs” defined by Cameron [P. J. Cameron, Discrete Math 309 (2009), 4835–4842], we define a new class of combinatorial designs which simultaneously provide a generalization of both covering designs and covering arrays. We then obtain a number of bounds on the minimum sizes of these designs, and describe some methods of constructing them, which in some cases we prove are optimal. Many of our results are obtained from an interpretation of these designs in terms of clique coverings of graphs. © 2011 Wiley Periodicals, Inc. J Combin Designs 19:378‐406, 2011 相似文献
20.
For every simple graph G,a class of multiple clique cluster-whiskered graphs Geπm is introduced,and it is shown that all such graphs are vertex decomposable;thus,the independence simplicial complex IndGeπm is sequentially Cohen-Macaulay.The properties of the graphs Geπm and Gπ constructed by Cook and Nagel are studied,including the enumeration of facets of the complex Ind Gπ and the calculation of Betti numbers of the cover ideal Ic(Geπ").We also prove that the complex △ =IndH is strongly shellable and pure for either a Boolean graph H =Bn or the full clique-whiskered graph H =Gw of G,which is obtained by adding a whisker to each vertex of G.This implies that both the facet ideal I(△) and the cover ideal Ic(H) have linear quotients. 相似文献