#### Title

The Average Order of a Subtree of a Tree

#### Document Type

Article

#### Publication Date

3-2010

#### Publication Title

Journal of Combinatorial Theory, Series B

#### DOI

10.1016/j.jctb.2009.05.006

#### ISSN

0095-8956

#### Abstract

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.

#### Recommended Citation

Vince, Andrew, Hua Wang.
2010.
"The Average Order of a Subtree of a Tree."
*Journal of Combinatorial Theory, Series B*, 100 (2): 161-170.
doi: 10.1016/j.jctb.2009.05.006

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/204