On the maximum size of minimal definitive quartet sets

Details On the maximum size of minimal definitive quartet sets On the maximum size of minimal definitive quartet sets

2011-01-27

arxiv.org/abs/1101.5302v1

Discrete Mathematics 310 (19), 2546-2549 (2010)

Mathematics

Combinatorics

7 pages, 5 figures

Scientific paper

10.1016/j.disc.2010.06.002

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.

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