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