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Blocking set free configurations and their relations to digraphs and hypergraphs - MaRDI portal

Blocking set free configurations and their relations to digraphs and hypergraphs (Q1356757)

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scientific article; zbMATH DE number 1019107
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English
Blocking set free configurations and their relations to digraphs and hypergraphs
scientific article; zbMATH DE number 1019107

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    Blocking set free configurations and their relations to digraphs and hypergraphs (English)
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    10 June 1997
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    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.
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    blocking set free configurations
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