On the graph labellings arising from phylogenetics
  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. 
Weronika Buczy\'nska, Jaros{\l}aw Buczy\'nski, Kaie Kubjas, Mateusz   Micha{\l}ek
math.CO math.AG