Transversals in uniform hypergraphs with property (7, 2)
type: Item
instance of: scholarly article
title: Transversals in uniform hypergraphs with property (7, 2)
zbMATH Open document ID: 0936.05071
DOI: 10.1016/S0012-365X(99)00114-4
author: Dmitry G. Fon-Der-Flaass
author: Douglas R. Woodall
author: Alexandr Kostochka
published in: Discrete Mathematics
publication date: 2000-02-22T00:00:00Z
review text: Let \(f(r,p,2)\) \((p> 1, r\geq 2)\) be the maximum of the cardinality of a minimum transversal over all \(r\)-uniform hypergraphs \(\mathcal{H}\) possessing the property that every subhypergraph of \(\mathcal{H}\) with \(p\) edges has a transversal of size \(2\). The values of \(f(r,p,2)\) for \(p=3,4,5,6\) were found by \textit{P. Erdős, D. Fon-Der-Flaass, A. V. Kostochka} and \textit{Zs. Tuza} [Sib. Adv. Math. 2, No. 1, 82-88 (1992; Zbl 0848.05049)]. The case \(p=7\) is much harder. The authors give some interesting bounds on \(f(r,7,2)\). In particular, they show that \(f(4k,7,2)\geq 3k+1\) for \(k \geq 10\) and that \(f(r,7,2)\leq \lceil 7r/8\rceil\).
reviewed by: Fedor V. Fomin
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 1382648
zbMATH Keywords: transversal
zbMATH Keywords: uniform hypergraph
MaRDI profile type: Publication
Wikidata QID: Q127481040
full work available at URL: s0012-365x(99)00114-4
OpenAlex ID: W2094192912
description: scientific article; zbMATH DE number 1382648