Trees with given degree sequences that have minimal subtrees

摘要

In this paper, we investigate the structures of an extremal tree which hasthe minimal number of subtrees in the set of all trees with the given degreesequence of a tree. In particular, the extremal trees must be caterpillar andbut in general not unique. Moreover, all extremal trees with a given degreesequence $\pi=(d_1, ..., d_5, 1,..., 1)$ have been characterized.