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Eva Czabarka: Universal rooted phylogenetic tree shape

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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 non-root vertices of X as subdividing
The resulting tree is a rooted binary tree that has X as one of its
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 n-universal, if it contains all n-leaf rooted binary trees as induced binary subtrees. Define the function u(n) as the minimum number of leaves in an n-universal 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


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