%0 Journal Article
%T Low degree minimal generators of phylogenetic semigroups
%A Kaie Kubjas
%J Mathematics
%D 2013
%I arXiv
%X The phylogenetic semigroup on a graph generalizes the Jukes-Cantor binary model on a tree. Minimal generating sets of phylogenetic semigroups have been described for trivalent trees by Buczy\'nska and Wi\'sniewski, and for trivalent graphs with first Betti number 1 by Buczy\'nska. We characterize degree two minimal generators of the phylogenetic semigroup on any trivalent graph. Moreover, for any graph with first Betti number 1 and for any trivalent graph with first Betti number 2 we describe the minimal generating set of its phylogenetic semigroup.
%U http://arxiv.org/abs/1304.0744v1