  A BC-tree (block-cutpoint-tree) is a tree (with at least two vertices) where
the distance between any two leaves is even. Motivated from the study of the
"core" of a graph, BC-trees provide an interesting class of trees. We consider
questions related to BC-trees as an effort to make modest progress towards the
understanding of this concept. Constructive algorithms are provided for
BC-trees with given order and number of leaves whenever possible. The concept
of BC-subtrees is naturally introduced. Inspired by analogous work on trees and
subtrees, we also present some extremal results and briefly discuss the "middle
part" of a tree with respect to the number of BC-subtrees.
