Directed Moore hypergraphs
For any directed hypergraph \(H\) with \(n\) vertices, maximum out-degree \(d^+\), maximum out-size \(s^+\) and diameter \(D\) we have \(n\leq \sum^D_{i= 0} (d^+ s^+)^i\). The authors prove a conjecture of Jean-Claude Bermond, which states that this bound cannot be attained if \(D> 1\) unless \(H\) is a directed cycle. Directed hypergraphs that attain this bound are called directed Moore hypergraphs. In addition, the authors prove that directed Moore hypergraphs can be identified with certain kinds of matrix factorizations.
scientific article; zbMATH DE number 822835
scientific article