Extremal results on average subtree density of series-reduced trees

Abstract

Vince and Wang showed that the average subtree density of a series-reduced tree is between 1/2 and 3/4, answering a conjecture of Jamison. They ask under what conditions a sequence of such trees may have average subtree density tending to either bound; we answer these questions by giving simple necessary and sufficient conditions in each case.Comment: 16 page