1-intersecting families
type: Item
instance of: scholarly article
title: 1-intersecting families
zbMATH Open document ID: 0572.05005
DOI: 10.1016/0012-365X(85)90132-3
author: M. C. Maurer
author: M. A. Habib
published in: Discrete Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The authors study combinatorial properties of subset families yielded by graph (or hypergraph) substitution decomposition and also by others combinatorial decomposition theories such as those studied by Cunningham and Edmonds. The main family \({\mathcal F}\) studied here (called 1- intersecting family) is made with subsets of a ground set X and satisfies: \(\emptyset,X\in {\mathcal F}\), for all \(A\in {\mathcal F}| A| \geq 2\), \(A\in {\mathcal F}\Rightarrow \bar A\in {\mathcal F}\), \(| A\cap B| >1\) and \(A\cup B\neq X\Rightarrow A\cap B\in {\mathcal F}.\) A characterization theorem and a recursive construction of 1-intersecting family are given.
Mathematics Subject Classification ID: 05A05
zbMATH DE Number: 3912386
zbMATH Keywords: subset families
zbMATH Keywords: substitution decomposition
zbMATH Keywords: combinatorial decomposition
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3912386