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arXiv · 2112.09663

The Edge-Product Space of Phylogenetic Trees is Not Shellable

Grace Stadnyk
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Abstract

The edge-product space of phylogenetic trees is a regular CW complex whose maximal closed cells correspond to trivalent trees with leaves labeled by a finite set $X$. The face poset of this cell decomposition is isomorphic to the Tuffley poset, a poset of labeled forests, with a unique minimum adjoined. We show that the edge-product space of phylogenetic trees is gallery-connected. We then use combinatorial properties of the Tuffley poset and a related graph known as NNI-tree space to show that, although open intervals of the Tuffley poset were proven to be shellable by Gill, Linusson, Moulton, and Steel, the edge-product space is not shellable.

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BibTeXRIS

Grace Stadnyk. 2022-03-19. The Edge-Product Space of Phylogenetic Trees is Not Shellable. https://doi.org/10.1016/j.aam.2021.102311

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