# Extremal Distances for Subtree Transfer Operations in Binary Trees

@article{Atkins2018ExtremalDF,
title={Extremal Distances for Subtree Transfer Operations in Binary Trees},
author={Ross Atkins and Colin McDiarmid},
journal={Annals of Combinatorics},
year={2018},
volume={23},
pages={1-26}
}
• Published 2 September 2015
• Mathematics, Computer Science
• Annals of Combinatorics
Three standard subtree transfer operations for binary trees, used in particular for phylogenetic trees, are: tree bisection and reconnection (TBR), subtree prune and regraft (SPR), and rooted subtree prune and regraft (rSPR). We show that for a pair of leaf-labelled binary trees with n leaves, the maximum number of such moves required to transform one into the other is $$n-\Theta (\sqrt{n})$$n-Θ(n), extending a result of Ding, Grünewald, and Humphries, and this holds also if one of the trees is…
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