%0 Journal Article
%T On the maximum quartet distance between phylogenetic trees
%A Noga Alon
%A Humberto Naves
%A Benny Sudakov
%J Computer Science
%D 2015
%I arXiv
%X A conjecture of Bandelt and Dress states that the maximum quartet distance between any two phylogenetic trees on $n$ leaves is at most $(\frac 23 +o(1))\binom{n}{4}$. Using the machinery of flag algebras we improve the currently known bounds regarding this conjecture, in particular we show that the maximum is at most $(0.69 +o(1))\binom{n}{4}$. We also give further evidence that the conjecture is true by proving that the maximum distance between caterpillar trees is at most $(\frac 23 +o(1))\binom{n}{4}$.
%U http://arxiv.org/abs/1505.04344v1