Low degree minimal generators of phylogenetic semigroups
arXiv:1304.0744
Abstract
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 Buczyńska and Wiśniewski, and for trivalent graphs with first Betti number 1 by Buczyńska. 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.