The maximum agreement subtree problem

Details The maximum agreement subtree problem The maximum agreement subtree problem

2012-01-25

arxiv.org/abs/1201.5168v2

Mathematics

Combinatorics

12 pages, 1 figure

Scientific paper

Given two binary phylogenetic trees on $n$ leaves, we show that they have a common subtree on at least $O((\log{n})^{1/2-\epsilon})$ leaves, thus improving on the previously known bound of $O(\log\log n)$. To achieve this bound, we combine different special cases: when one of the trees is balanced or when one of the trees is a caterpillar, we show a lower bound of $O(\log n)$. Another ingredient is the proof that every binary tree contains a large balanced subtree or a large caterpillar, a result that is intersting on its own. Finally, we also show that there is an $\alpha > 0$ such that when both the trees are balanced, they have a common subtree on at least $O(n^\alpha)$ leaves.

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