Blocking set free configurations and their relations to digraphs and hypergraphs
type: Item
instance of: scholarly article
title: Blocking set free configurations and their relations to digraphs and hypergraphs
zbMATH Open document ID: 0891.05016
DOI: 10.1016/S0012-365X(96)00183-5
author: Harald Gropp
published in: Discrete Mathematics
publication date: 1997-06-10T00:00:00Z
review text: The paper under review begins with a nice survey on the existence problem for blocking set free configurations. In his historical remarks, the author mentions the following interesting fact which I was certainly not aware of: The well-known theorem on the existence of a 1-factor in a regular bipartite graph (usually attributed to König) was actually obtained 20 years earlier by Steinitz in his Ph.D. thesis. The author also proves a new general result in the non-symmetric case: For each \(r\geq 3\), there is an integer \(\nu_0(r)\) such that a blocking set free configuration \((\nu_r, b_3)\) exists for \(\nu\geq \nu_0(r)\) provided that the necessary arithmetic existence conditions are satisfied.
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 51E30
Mathematics Subject Classification ID: 05C65
zbMATH DE Number: 1019107
zbMATH Keywords: blocking set free configurations
reviewed by: Dieter Jungnickel
MaRDI profile type: Publication
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Wikidata QID: Q127063910
full work available at URL: s0012-365x(96)00183-5
OpenAlex ID: W2017151232
description: scientific article; zbMATH DE number 1019107