On the number of Sperner vertices in a tree | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2016. № 2(32).

A vertex v of a tree T is called a Sperner vertex if the in-tree T(v) obtained from T by orientation of all edges towards v has the Sperner property, i.e. there exists a largest subset A of mutually unreachable vertices in it such that all vertices in A are equidistant to v. Some explicit methods to count the number of Sperner vertices in certain special trees are presented.