The EKR conjecture for induced subgraphs of perfect matchings

Let $M_n$ be the graph consisting of $n$ pairwise disjoint copies of $K_2$, and let $4\mathcal{H}^{(p,s)}(n)4$ be the family of induced subgraphs of $M_n$ consisting of $p$ disjoint edges and $s$ isolated vertices, where $s,p$ are non-negative integers and $1\leq 2p+s\leq n$. A family of members of $4\mathcal{H}^{(p,s)}(n)4$ is intersecting if any two of its members have a common vertex.

EKR conjecture. $4\mathcal{H}^{(p,s)}(n)4$ is EKR: every intersecting subfamily has size at most the size of a star, with equality attained by a family consisting of all members containing a fixed vertex of $M_n$.

This conjecture extends two distinct Erdős–Ko–Rado-type theorems to families of induced subgraphs of perfect matchings. The supplied text does not state whether it has been resolved.