I came up with this problem while thinking about an optimizing compiler.
Let $H$ be a hypergraph. From this we construct a graph $G_H$ as follows the vertices are the hyperedges of the hypergraph. There is an edge in $G_H$ whenever the hyperedges $e_1$ and $e_2$ have a vertex in $G$ in common.
I would like to know what I can say about the Cheeger constant of $G_H$.
In fact I have a family $H_n$, so this will go into whether there is a nonzero lower bound that works for all the $G_{H_n}$.
