Minimizing the number of matchings of fixed size in a $K_s$-saturated graph

Jiejing Feng, Doudou Hei, Xinmin Hou

For a fixed graph $F$, a graph $G$ is said to be $F$-saturated if $G$ does not contain a subgraph isomorphic to $F$ but does contain $F$ after the addition of any new edge. Let $M_…