Recent results on subtrees of trees

Stephan Wagner
Stellenbosch University

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Minisymposium: COMBINATORICS

Content: This talk reviews some recent results on the number of subtrees of a tree and related tree invariants. Specifically, we will be looking at extremal trees (maximising or minimising the number of subtrees) under various conditions, bounds on the average subtree order (average size of a randomly chosen subtree of a tree) that settle some conjectures of Jamison from the 1980s, the distribution of the subtree orders in "large" trees, and the number of nonisomorphic subtrees of a tree.

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