On the Extremal Maximum Agreement Subtree Problem

12/17/2018

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by   Alexey Markin, et al.

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Given two phylogenetic trees with the {1, ..., n} leaf-set the maximum agreement subtree problem asks what is the maximum size of the subset A ⊆{1, ..., n} such that the two trees are equivalent when restricted to A. The long-standing extremal version of this problem focuses on the smallest number of leaves, mast(n), on which any two (binary and unrooted) phylogenetic trees with n leaves must agree. In this work we prove that this number grows asymptotically as Θ( n); thus closing the enduring gap between the lower and upper asymptotic bounds on mast(n).