Which phylogenetic networks are merely trees with additional arcs?

Andrew R. Francis; Mike Steel

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arXiv · 1502.07045

Which phylogenetic networks are merely trees with additional arcs?

Andrew R. Francis·Mike Steel

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Abstract

A binary phylogenetic network may or may not be obtainable from a tree by the addition of directed edges (arcs) between tree arcs. Here, we establish a precise and easily tested criterion (based on `2-SAT') that efficiently determines whether or not any given network can be realized in this way. Moreover, the proof provides a polynomial-time algorithm for finding one or more trees (when they exist) on which the network can be based. A number of interesting consequences are presented as corollaries; these lead to some further relevant questions and observations, which we outline in the conclusion.

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Andrew R. Francis, Mike Steel. 2015-02-25. Which phylogenetic networks are merely trees with additional arcs?. https://arxiv.org/abs/1502.07045

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