The tree T(h)

Determine whether the tree T(h), formed from three complete binary trees of depth h with designated degree-2 vertices joined to a new common vertex, is r-EKR for every admissible r.

Background

The survey introduces T(h) as a test family in the study of trees whose interior vertices have degree 3. It arises from attempts to understand stronger center-location properties for trees without degree-2 vertices.

The survey explicitly asks whether this particular family satisfies the r-EKR property for all r.