Helly property in finite set systems
type: Item
instance of: scholarly article
title: Helly property in finite set systems
zbMATH Open document ID: 0773.05096
DOI: 10.1016/0097-3165(93)90068-J
published in: Journal of Combinatorial Theory. Series A
publication date: 1993-05-16T00:00:00Z
review text: This paper investigates the combinatorial counterparts of the famous Helly theorem: a finite set system satisfies the \(d\)-dimensional Helly property if every subsystem with empty intersection has a sub-subsystem of at most \(d+1\) elements with an empty intersection, again. Numerous extremal properties of \(d\)-dimensional Helly systems are proven including LYM-type inequalities. The results generalize several former theorems of B. Bollobás and P. Duchet. More open problems are formulated including a ``full'' LYM-type inequality.
Mathematics Subject Classification ID: 05D05
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 165747
zbMATH Keywords: Bollobas inequality
zbMATH Keywords: Sperner
zbMATH Keywords: convex hull
zbMATH Keywords: Helly theorem
zbMATH Keywords: finite set system
zbMATH Keywords: Helly property
zbMATH Keywords: LYM-type inequality
author: Zsolt Tuza
reviewed by: Péter L. Erdős
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 165747