Packing and covering k-chain free subsets in Boolean lattices (Q1043999)
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scientific article; zbMATH DE number 5644984
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Packing and covering k-chain free subsets in Boolean lattices |
scientific article; zbMATH DE number 5644984 |
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Packing and covering k-chain free subsets in Boolean lattices (English)
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10 December 2009
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The hypergraph \(H(B_n)\) is defined whose vertices are the points of the Boolean lattice \(B_n\) and whose edges are inclusionwise maximal \(k\)-chain free subsets of \(B_n\). In the paper under review, the author finds asymptotic bounds for the covering number (the smallest number of vertices intersecting every hyperedge) and the packing number (the greatest number of pairwise disjoint hyperedges) of \(H(B_n)\). Estimations were so far known only for \(k=2\).
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Boolean lattice
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maximal \(k\)-chain free subset
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packing number
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covering number
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