On the Largest Common Subtree of Random Leaf-Labeled Binary Trees

David J. Aldous

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arXiv · 2006.10545

On the Largest Common Subtree of Random Leaf-Labeled Binary Trees

David J. Aldous

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Abstract

The size of the largest common subtree (maximum agreement subtree) of two independent uniform random binary trees on $n$ leaves is known to be between orders $n^{1/8}$ and $n^{1/2}$. By a construction based on recursive splitting and analyzable by standard "stochastic fragmentation" methods, we improve the lower bound to order $n^\beta$ for $\beta = \frac{\sqrt{3} - 1}{2} = 0.366$. Improving the upper bound remains a challenging problem.

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David J. Aldous. 2020-06-18. On the Largest Common Subtree of Random Leaf-Labeled Binary Trees. https://arxiv.org/abs/2006.10545

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