Bounding the maximum size of a minimal definitive set of quartets

Dowden (2010) [2] showed that the maximum size of a minimal definitive set QQ of quartets is at least 2n−82n−8, for all n⩾4n⩾4, where n   is the size of the label set of QQ. In this paper, we show that the maximum size of such a set of quartets is at least Ω(n2)Ω(n2) and, moreover, is strictly less than n3n3, for all n⩾4n⩾4.

► We investigate the maximum size of a minimal definitive set of quartets.
► Previous results showed it is at least linear in the size of the label set.
► We show it is at least quadratic and at most cubic in the size of the label set.