### Abstract

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 language | English (US) |
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Pages (from-to) | 718-735 |

Number of pages | 18 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 30 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2016 |

### Keywords

- Flag algebras
- Phylogenetic trees
- Quartet distance

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## Cite this

Alon, N., Naves, H., & Sudakov, B. (2016). On the maximum quartet distance between phylogenetic trees.

*SIAM Journal on Discrete Mathematics*,*30*(2), 718-735. https://doi.org/10.1137/15M1041754