On Agreement Subtrees in Multiple Pylogenetic Trees

Bryan Currie; Éva Czabarka; Mareike Fischer; Henry Simmons; László Székely; Kristina Wicke

On Agreement Subtrees in Multiple Pylogenetic Trees

Combinatorics 2026-07-14 v1

Authors: Bryan Currie , Éva Czabarka , Mareike Fischer , Henry Simmons , László Székely , Kristina Wicke

Abstract

Snir and Yuster [Discrete Appl. Math. 347 (2026) 160--171] asked for the least number $h(k)$ such that $k$ unrooted binary phylogenetic trees on the same $h(k)$ leaves always share a common quartet. We give a new upper bound for the $k$ -tree version of the Maximum Agreement Subtree problem, namely an upper bound for the number of leaves, on which $k$ unrooted binary phylogenetic trees always share a common induced binary subtree on $n$ leaves, which is a four-times iterated exponential function. For $h(k)$ , this implies a four-times iterated exponential upper bound. We also set an exponential lower bound for $h(k)$ .

Cite

@article{arxiv.2607.12778,
  title  = {On Agreement Subtrees in Multiple Pylogenetic Trees},
  author = {Bryan Currie and Éva Czabarka and Mareike Fischer and Henry Simmons and László Székely and Kristina Wicke},
  journal= {arXiv preprint arXiv:2607.12778},
  year   = {2026}
}