منابع مشابه
Sparse universal graphs
For every n, we describe an explicit construction of a graph on n vertices with at most O(n2− ) edges, for = 0.133 . . ., that contains every graph on n vertices with maximum degree 3 as a subgraph. It is easy to see that each such graph must have at least Ω(n 4 3 ) edges. We also show that the minimum number of edges of a graph that contains every graph with n edges as a subgraph is Θ( n 2 log...
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Let H be a family of graphs. A graph T is H-universal if it contains a copy of each H ∈ H as a subgraph. Let H(k, n) denote the family of graphs on n vertices with maximum degree at most k. For all positive integers k and n, we construct an H(k, n)-universal graph T with Ok(n 2 k log 4 k n) edges and exactly n vertices. The number of edges is almost as small as possible, as Ω(n2−2/k) is a lower...
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In 1983, Chvátal, Trotter and the two senior authors proved that for any ∆ there exists B so that, for any n, any 2-coloring of the edges of the complete graph KN with N ≥ Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree ∆. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N2−1/∆ log N) edges, with N = bB...
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Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many signal and image processing tasks. It is now well understood that the choice of the sparsity regularization term is critical in the success of such models. In th...
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This paper investigates the class of k universal nite graphs a local analog of the class of universal graphs which arises naturally in the study of nite variable logics The main results of the paper which are due to Shelah establish that the class of k universal graphs is not de nable by an in nite disjunction of rst order existential sentences with a nite number of variables and that there exi...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2002
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(01)00455-1