On the graph labellings arising from phylogenetics

Abstract

We study semigroups of labellings associated to a graph. These generalize the Jukes-Cantor model and phylogenetic toric varieties defined by Buczyńska. 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.

17 pages, 13 figures; v2: presentation improved, results generalised to arbitrary graphs (not only trivalent); to appear in Central European Journal of Mathematics

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