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).
Bibliographical noteFunding Information:
Sackler School of Mathematics and Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel, and School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540 (firstname.lastname@example.org). This author's research was supported in part by a USA-Israeli BSF grant, an ISF grant, the Israeli I-Core program, and the Fund for Mathematics.
© 2016 Society for Industrial and Applied Mathematics.
- Flag algebras
- Phylogenetic trees
- Quartet distance