Minimal regular 2-graphs and applications (Q854642)

A 2-graph is a hypergraph with edge sizes at most two. It is minimal if it does not contain a proper regular factor. Let \(f_2(n)\) be the maximum value of degrees over all minimal 2-graphs of \(n\) vertices. In this paper the authors prove that \(f_2(n) = \frac{n+3-i}{3}\), for \(n \geq 7\) and \(i = n \pmod 6\). This can be used in graph theory to characterize unfactorable regular graphs and to provide the best possible factor existence theorem on degree conditions.