The covering problem of complete uniform hypergraphs
نویسندگان
چکیده
منابع مشابه
Improved 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 ...
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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...
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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...
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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 کاملThe α-Arboricity of Complete Uniform Hypergraphs
α-acyclicity is an important notion in database theory. The α-arboricity of a hypergraphH is the minimum number of α-acyclic hypergraphs that partition the edge set of H. The α-arboricity of the complete 3-uniform hypergraph is determined completely.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1979
ISSN: 0012-365X
DOI: 10.1016/0012-365x(79)90074-8