Regular spanning subgraphs of bipartite graphs of high minimum degree

Abstract

Let G be a simple balanced bipartite graph on $2n$ vertices, $\delta =\delta (G)/n$, and $\rho =\frac{\delta +\sqrt{2\delta -1}}{2}$. If $\delta >1/2$ then it has a $\lfloor \rho n\rfloor$-regular spanning subgraph. The statement is nearly tight.

submitted