On the graph labellings arising from phylogenetics
Combinatorics
2016-05-19 v2 Algebraic Geometry
Abstract
We study semigroups of labellings associated to a graph. These generalize the Jukes-Cantor model and phylogenetic toric varieties defined by Buczy\'nska. Our main theorem bounds the degree of the generators of the semigroup by g+1 when the graph has first Betti number g. Also, we provide a series of examples where the bound is sharp.
Keywords
Cite
@article{arxiv.1105.5382,
title = {On the graph labellings arising from phylogenetics},
author = {Weronika Buczyńska and Jarosław Buczyński and Kaie Kubjas and Mateusz Michałek},
journal= {arXiv preprint arXiv:1105.5382},
year = {2016}
}
Comments
17 pages, 13 figures; v2: presentation improved, results generalised to arbitrary graphs (not only trivalent); to appear in Central European Journal of Mathematics