A fundamental problem in the study of phylogenetic networks is how to determine whether a phylogenetic network displays a phylogenetic tree or not. We develop a quadratic-time algorithm for this problem for binary nearly-stable phylogenetic networks. We also show that the number of reticulations in a reticulation visible or nearly stable phylogenetic network is bounded by a linear function of the number of taxa.
Philippe Gambette, Andreas D. M. Gunawan, Anthony