The Average Order of a Subtree of a Tree
Journal of Combinatorial Theory, Series B
Let T be a tree all of whose internal vertices have degree at least three. In 1983 Jamison conjectured in JCT B that the average order of a subtree of T is at least half the order of T. In this paper a proof is provided. In addition, it is proved that the average order of a subtree of T is at most three quarters the order of T. Several open questions are stated.
Vince, Andrew, Hua Wang.
"The Average Order of a Subtree of a Tree."
Journal of Combinatorial Theory, Series B, 100 (2): 161-170.