منابع مشابه
Covering Non-uniform Hypergraphs
A subset of the vertices in a hypergraph is a cover if it intersects every edge. Let τ(H) denote the cardinality of a minimum cover in the hypergraph H , and let us denote by g(n) the maximum of τ(H) taken over all hypergraphs H with n vertices and with no two hyperedges of the same size. We show that g(n) < 1.98 √ n(1 + o(1)). A special case corresponds to an old problem of Erdős asking the ma...
متن کاملCodegree Thresholds for Covering 3-Uniform Hypergraphs
Given two 3-uniform hypergraphs F and G = (V,E), we say that G has an F -covering if we can cover V with copies of F . The minimum codegree of G is the largest integer d such that every pair of vertices from V is contained in at least d triples from E. Define c2(n, F ) to be the largest minimum codegree among all n-vertex 3-graphs G that contain no F -covering. Determining c2(n, F ) is a natura...
متن کاملImproved Bounds for Covering Complete Uniform Hypergraphs
We consider the problem of covering the complete r-uniform hypergraphs on n vertices using complete r-partite graphs. We obtain lower bounds on the size of such a covering. For small values of r our result implies a lower bound of Ω( e r r √ r n log n) on the size of any such covering. This improves the previous bound of Ω(rn log n) due to Snir [5]. We also obtain good lower bounds on the size ...
متن کاملCovering symmetric supermodular functions by uniform hypergraphs
We consider the problem of finding a uniform hypergraph that satisfies cut demands defined by a symmetric crossing supermodular set function. We give min-max formulas for both the degree specified and the minimum cardinality problem. These results include as a special case a formula on the minimum number of r-hyperedges whose addition to an initial hypergraph will make it k-edge-connected.
متن کاملMixed Covering Arrays on 3-Uniform Hypergraphs
Covering arrays are combinatorial objects that have been successfully applied in the design of test suites for testing systems such as software, circuits and networks, where failures can be caused by the interaction between their parameters. In this paper, we perform a new generalization of covering arrays called covering arrays on 3-uniform hypergraphs. Let n, k be positive integers with k ≥ 3...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2001
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2037