On the length of a partial independent transversal in a matroidal Latin square (Q426878)
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scientific article; zbMATH DE number 6045705
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the length of a partial independent transversal in a matroidal Latin square |
scientific article; zbMATH DE number 6045705 |
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On the length of a partial independent transversal in a matroidal Latin square (English)
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12 June 2012
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Summary: We suggest and explore a matroidal version of the Brualdi-Ryser conjecture about Latin squares. We prove that any \(n\times n\) matrix, whose rows and columns are bases of a matroid, has an independent partial transversal of length \(\lceil2n/3\rceil\). We show that for any \(n\), there exists such a matrix with a maximal independent partial transversal of length at most \(n-1\).
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Latin square
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matroidal Latin square
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partial independent transversal
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