Meshkat–Sullivant's collapsed-graph conjecture for expected dimension

Let $G$ be a graph with $n$ vertices, $2n-2$ edges, and an exchange with $i$. The collapsed graph $G'$ is obtained by identifying vertices $1$ and $i$. Assume that $G'$ has $2n-4$ edges with an exchange. Meshkat–Sullivant's conjecture. The graph $G$ has the expected dimension if and only if $G'$ has the expected dimension. This conjecture relates expected dimension under collapsing an exchange and is presented as an extension of preceding results on graph constructions; its resolution is not specified in the source.