On the maximum quartet distance between phylogenetic trees

Noga Alon, Humberto Naves, Benny Sudakov

A conjecture of Bandelt and Dress states that the maximum quartet distance between any two phylogenetic trees on $n$ leaves is at most $(\frac{2}{3}+o(1))\left(\genfrac{}{}{0ex}{}{n}{4}\right)$. Using the mac…