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arXiv · 2602.07426

Maximally probable tree topologies with $r$-furcation

Emily H. Dickey·Noah A. Rosenberg
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Abstract

For a specific rooted labeled tree topology, a labeled history is a sequence of branchings that give rise to that labeled topology as it unfolds over time. Here, for $r$-furcating trees, we use a connection with Huffman trees from information theory to identify maximally probable rooted trees -- unlabeled $r$-furcating topologies whose labelings each have a number of labeled histories greater than or equal to those of all other labeled topologies. Our characterization of the unique maximally probable $r$-furcating unlabeled topology generalizes the Harding--Hammersley--Grimmett result identifying the maximally probable bifurcating unlabeled topology, and it provides a new proof for that result. We present a conjecture for the maximally probable $r$-furcating unlabeled topology if labeled histories are tabulated allowing for simultaneous branching events across multiple internal nodes of a tree.

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Emily H. Dickey, Noah A. Rosenberg. 2026-02-07. Maximally probable tree topologies with $r$-furcation. https://arxiv.org/abs/2602.07426

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