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Eva Czabarka: Universal rooted phylogenetic tree shape 



Friday, 19. May 2023, 13:00  13:30


A subset S of the leaves of a rooted binary tree T induces a rooted binary tree by the following procedure: (1) take the minimal subtree X of T that contains S, (2) designate the vertex closest to the original root as the root of X, and then (3) suppress the degree 2 nonroot vertices of X as subdividing vertices. The resulting tree is a rooted binary tree that has X as one of its subdivisions. A rooted binary tree T’ is an induced binary subtree of the rooted binary tree T if it is induced this way by some subset of the leaves. Given a positive integer n, a tree T is called nuniversal, if it contains all nleaf rooted binary trees as induced binary subtrees. Define the function u(n) as the minimum number of leaves in an nuniversal tree. We show that for some positive constants C, D, Cn log(n) < u(n)< Dn^2.
This work is part of a MRC 2022 project, done in collaboration with Ann Clifton, Kevin Liu, Sarah Loeb, Laszlo Szekely, Okur Utku and Kristina Wicke. 
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