Abstract:Let T be an arbitrary phylogenetic tree with n leaves. It is well-known that the average quartet distance between two assignments of taxa to the leaves of T is 2 3 n 4 . However, a longstanding conjecture of Bandelt and Dress asserts that ( 2 3 + o(1)) n 4 is also the maximum quartet distance between two assignments. While Alon, Naves, and Sudakov have shown this indeed holds for caterpillar trees, the general case of the conjecture is still unresolved. A natural extension is when partial information is given:… Show more
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