On the maximum quartet distance between phylogenetic trees

Noga Alon, Humberto Naves, Benny Sudakov

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish
Pages (from-to)718-735
Number of pages18
JournalSIAM Journal on Discrete Mathematics
Issue number2
StatePublished - 2016


FundersFunder number
Israeli I-Core program
Sackler School of Mathematics and Blavatnik School of Computer Science, Tel Aviv University
USA-Israeli BSF
Israel Science Foundation


    • Flag algebras
    • Phylogenetic trees
    • Quartet distance


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