On the number of \(F\)-matchings in a tree (Q426809)
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scientific article; zbMATH DE number 6045667
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of \(F\)-matchings in a tree |
scientific article; zbMATH DE number 6045667 |
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On the number of \(F\)-matchings in a tree (English)
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12 June 2012
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Summary: We prove that for any integers \(k,m>0\) and any tree \(F\) with at least one edge, there exists a tree whose number of \(F\)-matchings is congruent to \(k\) modulo \(m\) as well as an analogous result for induced \(F\)-matchings. This answers a question of \textit{N. Alon}, \textit{S. Haber} and \textit{M. Krivelevich} [``The number of \(F\)-matchings in almost every tree is a zero residue'', ibid. 18, No. 1, Research Paper P30, 10 p., electronic only (2011)].
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random labeled tree
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