Covering symmetric supermodular functions by uniform hypergraphs
نویسندگان
چکیده
منابع مشابه
Covering 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.
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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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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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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2004
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2003.12.004