On tactical configurations, regular bipartite graphs, and (v, k, even)-designs Original Research Article

A report on small regular bipartite graphs is given. Some historical facts are mentioned as well as equivalent combinatorial structures are discussed. In the second part a new combinatorial structure, the (v, k, even/odd)-designs are introduced. Some first results on (v, k, even)-designs for even k are obtained. Especially, all (v, 4, even)-designs are determined. For greater k certain interesting examples are given.