A note on \(K_{k,k}\)-cross free families (Q1010699)
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scientific article; zbMATH DE number 5540901
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on \(K_{k,k}\)-cross free families |
scientific article; zbMATH DE number 5540901 |
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A note on \(K_{k,k}\)-cross free families (English)
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7 April 2009
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Summary: We give a short proof that for any fixed integer \(k\), the maximum size of a \(K_{k,k}\)-cross free family is linear in the size of the groundset. We also give tight bounds on the maximum size of a \(K_k\)-cross free family in the case when \({\mathcal F}\) is intersecting or an antichain.
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maximum size
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\(K_{k,k}\)-cross free family
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intersecting family
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antichain
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0.8570723533630371
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0.8378689289093018
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0.8102474212646484
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0.7998751401901245
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