On a class of strong valid inequalities for the connected matching polytope

We identify a family of $O(\mathrm{\mid }E(G){\mathrm{\mid }}^2)$ nontrivial facets of the connected matching polytope of a graph $G$, that is, the convex hull of incidence vectors of matchings in $G$ whose covered vertices induce a connected subgraph. Accompanying software to further inspect the polytope of an input graph is available.