On the Extremal Maximum Agreement Subtree Problem

Alexey Markin

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arXiv · 1812.06951

On the Extremal Maximum Agreement Subtree Problem

Alexey Markin

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Abstract

Given two phylogenetic trees with the $\{1, \ldots, n\}$ leaf-set the maximum agreement subtree problem asks what is the maximum size of the subset $A \subseteq \{1, \ldots, n\}$ 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, $\mathrm{mast}(n)$, 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 $\Theta(\log n)$; thus closing the enduring gap between the lower and upper asymptotic bounds on $\mathrm{mast}(n)$.

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Alexey Markin. 2018-12-17. On the Extremal Maximum Agreement Subtree Problem. https://arxiv.org/abs/1812.06951

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