On the maximum quartet distance between phylogenetic trees

A conjecture of Bandelt and Dress states that the maximum quartet distance between any two phylogenetic trees on n leaves is at most (2 3 + o(1)) 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)) n 4 . We also give further evidence that the conjecture is true by proving that the maximum distance between caterpillar trees is at most (2 3 + o(1)) n 4 .

• Type: Journal
• Year: 2016
• Where: SODA
• Authors: Noga Alon, Humberto Naves, Benny Sudakov
• Keywords: Algorithms, SODA 2016