On the maximum size of minimal definitive quartet sets
arXiv:1101.5302 · doi:10.1016/j.disc.2010.06.002
Abstract
In this paper, we investigate a problem concerning quartets, which are a particular type of tree on four leaves. Loosely speaking, a set of quartets is said to be `definitive' if it completely encapsulates the structure of some larger tree, and `minimal' if it contains no redundant information. Here, we address the question of how large a minimal definitive quartet set on n leaves can be, showing that the maximum size is at least 2n-8 for all n>3. This is an enjoyable problem to work on, and we present a pretty construction, which employs symmetry.
7 pages, 5 figures