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arXiv · 2312.01190

The likely maximum size of twin subtrees in a large random tree

Miklos Bona·Ovidiu Costin·Boris Pittel
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Abstract

We call a pair of vertex-disjoint, induced subtrees of a rooted trees twins if they have the same counts of vertices by out-degrees. The likely maximum size of twins in a uniformly random, rooted Cayley tree of size $n\to\infty$ is studied. It is shown that the expected number of twins of size $(2+δ)\sqrt{\log n\cdot\log\log n}$ approaches zero, while the expected number of twins of size $(2-δ)\sqrt{\log n\cdot\log\log n}$ approaches infinity.

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Miklos Bona, Ovidiu Costin, Boris Pittel. 2024-06-05. The likely maximum size of twin subtrees in a large random tree. https://arxiv.org/abs/2312.01190

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