# PLG

## Seminar

### On the Complexity of the Quartet Challenge

Seminar Room 1, Newton Institute

#### Abstract

A collection of quartets (unrooted phylogenetic trees on four taxa) is compatible if there exists a phylogenetic tree that explains all ancestral relationships given by the quartets. It is well-known that deciding whether or not a set of quartets is compatible is an NP-complete problem. A natural extension of this problem asks if, given a phylogenetic tree T that is compatible with the input, is T the only such tree. Several graph-theoretic characterizations have been established to approach this problem, which is known as the Quartet Challenge. However, the complexity of this challenge remains open. In this talk, we show that the Quartet Challenge is ASP-complete (i.e. it is computationally hard to decide whether another solution exists) by using a particular type of polynomial-time reduction from a variation of the Betweenness problem. This is joint work with Maria Luisa Bonet (UPC, Spain) and Katherine St. John (CUNY, USA).#### Video

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