Hassler–Treglown conjecture on maximal independent sets in graphs with a perfect matching

Let $\Gamma$ be an $n$-vertex graph, and let $\mathrm{mis}(\Gamma)$ denote its number of maximal independent sets. Hassler–Treglown conjecture. If $\Gamma$ contains a perfect matching, then

$$\mathrm{mis}(\Gamma)\leq 2^{n/2}.$$

The abstract states that this conjecture is resolved by the paper’s graph-theoretic bound.