# Vertex percolation on bipartite graphs

This is essentially a repost of this math overflow post since it didn't get any reception.

Let $$G = (V \cup C, \mathcal{E})$$ be $$(\gamma_V, \delta_A, \gamma_B, \delta_B)$$-left-right-expanding with left degree bounded above by $$d_V$$ and right degree bounded above by $$d_C$$. I want to randomly select a subset $$R \subset C$$ and remove these vertices as well as any edges coming from $$R$$ from the graph. We then consider the induced subgraph $$G' = (V, C \backslash R, \mathcal{E}')$$.

The question is asking about the expansion properties of $$G'$$, i.e. is $$G'$$ still left-expanding, right-expanding, or both. Additionally, what can we say about the number and size of the connected components in $$G'$$? There has been work done on vertex percolation of $$d$$-regular expanders, but I can't see how this applies in the bipartite case.