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排序方式: 共有238条查询结果,搜索用时 31 毫秒
51.
对于每一个含有最小元素0的偏序集(P,≤)可以得到一个与其关联的图G(P).本文主要通过代数的方法研究了所得关联图G(P)的性质,证明了如果G(P)的色数和团数是有限的,那么色数和团数都仅比P的极小素理想的个数大1. 相似文献
52.
Jia Shen 《Journal of Graph Theory》2010,63(4):300-310
Given a “forbidden graph” F and an integer k, an F‐avoiding k‐coloring of a graph G is a k‐coloring of the vertices of G such that no maximal F‐free subgraph of G is monochromatic. The F‐avoiding chromatic number acF(G) is the smallest integer k such that G is F‐avoiding k‐colorable. In this paper, we will give a complete answer to the following question: for which graph F, does there exist a constant C, depending only on F, such that acF(G) ? C for any graph G? For those graphs F with unbounded avoiding chromatic number, upper bounds for acF(G) in terms of various invariants of G are also given. Particularly, we prove that ${{ac}}_{{{F}}}({{G}})\le {{2}}\lceil\sqrt{{{n}}}\rceil+{{1}}Given a “forbidden graph” F and an integer k, an F‐avoiding k‐coloring of a graph G is a k‐coloring of the vertices of G such that no maximal F‐free subgraph of G is monochromatic. The F‐avoiding chromatic number acF(G) is the smallest integer k such that G is F‐avoiding k‐colorable. In this paper, we will give a complete answer to the following question: for which graph F, does there exist a constant C, depending only on F, such that acF(G) ? C for any graph G? For those graphs F with unbounded avoiding chromatic number, upper bounds for acF(G) in terms of various invariants of G are also given. Particularly, we prove that ${{ac}}_{{{F}}}({{G}})\le {{2}}\lceil\sqrt{{{n}}}\rceil+{{1}}$, where n is the order of G and F is not Kk or $\overline{{{K}}_{{{k}}}}$. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 300–310, 2010 相似文献
53.
《Journal of Graph Theory》2018,89(3):288-303
A gem is a graph that consists of a path on four vertices plus a vertex adjacent to all four vertices of the path. A co‐gem is the complement of a gem. We prove that every (gem, co‐gem)‐free graph G satisfies the inequality (a special case of a conjecture of Gyárfás) and the inequality (a special case of a conjecture of Reed). Moreover, we give an ‐time algorithm that computes the chromatic number of any (gem, co‐gem)‐free graph with n vertices, while the existing algorithm in the literature takes . 相似文献
54.
《Journal of Graph Theory》2018,89(3):304-326
A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic number of a graph is large enough, either the graph contains a clique of size k or it contains T as an induced subgraph. We discuss some results and open problems about extensions of this conjecture to oriented graphs. We conjecture that for every oriented star S and integer k, if the chromatic number of a digraph is large enough, either the digraph contains a clique of size k or it contains S as an induced subgraph. As an evidence, we prove that for any oriented star S, every oriented graph with sufficiently large chromatic number contains either a transitive tournament of order 3 or S as an induced subdigraph. We then study for which sets of orientations of P4 (the path on four vertices) similar statements hold. We establish some positive and negative results. 相似文献
55.
Wayne Pullan 《Journal of Heuristics》2008,14(2):117-134
This paper extends the recently introduced Phased Local Search (PLS) algorithm to more difficult maximum clique problems and
also adapts the algorithm to handle maximum vertex/edge weighted clique instances. PLS is a stochastic reactive dynamic local
search algorithm that interleaves sub-algorithms which alternate between sequences of iterative improvement, during which
suitable vertices are added to the current sub-graph, and plateau search, where vertices of the current sub-graph are swapped
with vertices not contained in the current sub-graph. These sub-algorithms differ in firstly their vertex selection techniques
in that selection can be solely based on randomly selecting a vertex, randomly selecting within highest vertex degree, or
random selecting within vertex penalties that are dynamically adjusted during the search. Secondly, the perturbation mechanism
used to overcome search stagnation differs between the sub-algorithms. PLS has no problem instance dependent parameters and
achieves state-of-the-art performance for maximum clique and maximum vertex/edge weighted clique problems over a large range
of the commonly used DIMACS benchmark instances. 相似文献
56.
Evangelos Triantaphyllou 《Journal of Global Optimization》1994,5(1):69-94
This paper deals with the problem of identifying a hidden Boolean function : 0, 1' 0, 1 from positive and negative examples. This problem is of paramount importance in many real life applications of artificial intelligence. The method proposed in this paper is based on a branch-and-bound approach. This approach is an expansion of some earlier work (Triantaphyllouet al., 1994). Computational results, comparing the new method with one based on Karmakar's interior point method, suggest that the new method is very efficient. 相似文献
57.
58.
In this short note we obtain the full set of inequalities that define the convex hull of a 0–1 knapsack constraint presented
in Weismantel (1997). For that purpose we use our O(n) procedures for identifying maximal cliques and non-dominated extensions
of consecutive minimal covers and alternates, as well as our schemes for coefficient increase based tightening cover induced
inequalities and coefficient reduction based tightening general 0–1 knapsack constraints. 相似文献
59.
在经典排序论中,一般都作以下两条假设:其一是每台机器在任一时刻至多加工一个零件,其二是每个零件在任一时刻至多被一台机器加工.在这篇文章中,研究多台机器可同时加工一个零件的多机排序问题,且每个零件可在固定的一个机器的子集上加工.本文在机器总数确定,零件加工可间断的条件下,设计出求这类问题最优解的计算方法,并研究了这种问题的计算复杂性. 相似文献
60.