Degrees of generators of phylogenetic semigroups on graphs
Weronika Buczyńska · arXiv (Cornell University) · 2011
We study the phylogenetic semigroups associated to trivalent graphs introduced by Buczynska and related to works of Wisniewski, Sturmfels, Xu, Manon, Jeffrey, Weits- mann. Our main theorem bounds the degree of the generators of a semigroup associated with a graph with first Betti number g by g + 1. Furthermore, this bound is effective for many graphs. In particular, the caterpillar graph with g loops has generators of degree g + 1 for even g and of degree g for odd g.