Hiu-Fai Law, F-Matchings in a tree

Given trees F and T, a F-matching is a collection of disjoint copies F in T. Generalizing results from Wagner (2009), Alon et al (2011) proved that the number of F-matchings for fixed F in a random tree T whose size tends to infinity is a.a.s. a multiple of any given integer m>0. We will discuss inverse and extremal problems on the number of F-matchings.