A uniformly random $r$-regular bipartite graph on $n$ vertices is known to be $r$-edge connected. That is, with high probability as $n$ grows large, the minimum size of a cut in a random $r$-regular bipartite graph is $r$.

I was wondering if there is a similar statement for the following small extension: Is a uniformly random $(r+1,r)$-biregular bipartite graph almost surely $r$-edge connected?

An $(r+1,r)$-biregular bipartite graph is a bipartite graph where the left side vertices all have degree $r+1$, and the right side vertices have degree $r$.

It seems very reasonable that this extension is true since the graph has a higher density of edges than the $r$-regular case.

Thank you