Hypergraph families with bounded edge cover or transversal number
type: Item
instance of: scholarly article
title: Hypergraph families with bounded edge cover or transversal number
zbMATH Open document ID: 0534.05052
DOI: 10.1007/BF02579191
author: N. E. Zubov
published in: Combinatorica
publication date: 1983-01-01T00:00:00Z
review text: The transversal number \(\tau\), packing number \(\nu\), covering number \(\rho\), and strong stability number \(\alpha\) of hypergraphs are studied. A family F of finite hypergraphs is \(\tau\)-bound (\(\rho\)-bound) if there exists a binding function f such that \(\tau\) (H)\(\leq f(\nu(H))\) (\(\rho\) (H)\(\leq f(\alpha(H)))\) for all \(H\in F\). The existence of a binding function in case of various \(\tau\)-bound (\(\rho\)-bound) is given. It is essentially based on the exclusion of octahedron graphs. Hypergraph versions of the clique color theorem of \textit{A. Gyárfás} [Infinite finite sets, Colloq. Honour Paul Erdős, Keszthely 1973, Colloq. Math. Soc. János Bolyai 10, 801-816 (1975; Zbl 0307.05111)] are presented. Further results concern Helly hypergraphs with \(C_ 4\)-free line-graph, c-forest hypergraphs, strong Helly hypergraphs, boxes, and polyominoes (cf. the paper of \textit{C. Berge}, \textit{C. C. Chen}, \textit{V. Chvátal} and \textit{C. S. Seow} [Combinatorica 1, 217-224 (1981; Zbl 0491.05048)]).
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05B40
zbMATH DE Number: 3847440
zbMATH Keywords: transversal number
zbMATH Keywords: packing number
zbMATH Keywords: covering number
zbMATH Keywords: strong stability number
zbMATH Keywords: Helly hypergraphs
reviewed by: Ján Plesník
MaRDI profile type: Publication
cites work: Combinatorial properties of polyominoes
cites work: Graph Theory and Probability. II
cites work: On chromatic number of graphs and set-systems
cites work: Hypergraphes arbores
cites work: A Ramsey-type theorem and its application to relatives of Helly's theorem
full work available at URL: https://doi.org/10.1007/bf02579191
OpenAlex ID: W2047637845
description: scientific article; zbMATH DE number 3847440