A uniformly random $r$-regular bipartite graph 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?
A biregular graph is a bipartite graph where the left side is regular, and the right side is also regular but with a different degree.
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!