We study semigroups of labellings associated to a graph. These generalise the Jukes-Cantor model and phylogenetic toric varieties defined in [Buczynska W., Phylogenetic toric varieties on graphs, J. Algebraic Combin., 2012, 35(3), 421–460]. 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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0263-3,
author = {Weronika Buczy\'nska and Jaros\l aw Buczy\'nski and Kaie Kubjas and Mateusz Micha\l ek},
title = {On the graph labellings arising from phylogenetics},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1577-1592},
zbl = {1282.14087},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0263-3}
}
Weronika Buczyńska; Jarosław Buczyński; Kaie Kubjas; Mateusz Michałek. On the graph labellings arising from phylogenetics. Open Mathematics, Tome 11 (2013) pp. 1577-1592. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0263-3/
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