### 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(l))(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(l)) (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 +0(1))(n/4).

Original language | English (US) |
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Title of host publication | 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 |

Editors | Robert Krauthgamer |

Publisher | Association for Computing Machinery |

Pages | 2095-2106 |

Number of pages | 12 |

ISBN (Electronic) | 9781510819672 |

DOIs | |

State | Published - 2016 |

Externally published | Yes |

Event | 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 - Arlington, United States Duration: Jan 10 2016 → Jan 12 2016 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | 3 |

### Other

Other | 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 |
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Country | United States |

City | Arlington |

Period | 1/10/16 → 1/12/16 |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

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## Cite this

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

*27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016*(pp. 2095-2106). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 3). Association for Computing Machinery. https://doi.org/10.1137/1.9781611974331.ch146