Let $\Delta$ be a simplicial complex and $F, G$ be two facets of $\Delta$. We say that $F$ and $G$ form a gap in $\Delta$ if $F \cap G = \emptyset$ and the induced subcollection on the vertex set $F \cup G$ is exactly $\langle F, G \rangle$. A matching $M$ of $\Delta$ is called a restricted matching if there exists a facet in $M$ that forms a gap with every other facet in $M$. The maximal size of a restricted matching of $\Delta$ is called the restricted matching number of $\Delta$.
My question. In SageMath, Macaulay2, or other software, is there any known algorithm to compute the restricted matching number of a simplicial complex, or at least of a graph (i.e., a $1$-dimensional simplicial complex)?