A counterexample to Aharoni's strongly maximal matching conjecture (Q1910586)
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scientific article; zbMATH DE number 858118
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A counterexample to Aharoni's strongly maximal matching conjecture |
scientific article; zbMATH DE number 858118 |
Statements
A counterexample to Aharoni's strongly maximal matching conjecture (English)
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25 March 1996
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Aharoni conjectured that in every family \(A\) of finite sets a subfamily \(B\) of disjoint sets exists, so that no replacement of \(k\) of them by more than \(k\) sets from \(A\) results again in a subfamily of disjoint sets. The authors present as a counterexample the family of those finite subets of the set of natural numbers whose cardinality and smallest element coincide.
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strongly maximal matching
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Aharoni's conjecture
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infinite hypergraph
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counterexample
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