Small \(2\)-factors of Bipartite Graphs

A \(2\)-factor \(F\) of a bipartite graph \(G = (A, B; E)\), \(|A| = |B| = n\), is small if \(F\) comprises \(\lfloor \frac{n}{2}\rfloor\) cycles. A set \(\mathfrak{F}\) of small edge-disjoint \(2\)-factors of \(G\) is maximal if \(G – \mathfrak{F}\) does not contain a small \(2\)-factor. We study the spectrum of maximal sets of small \(2\)-factors.