Degrees of generators of phylogenetic semigroups on graphs

Details Degrees of generators of phylogenetic semigroups on graphs Degrees of generators of phylogenetic semigroups on graphs

2011-05-26

arxiv.org/abs/1105.5382v1

Mathematics

Combinatorics

Scientific paper

We study the phylogenetic semigroups associated to trivalent graphs introduced by Buczy\'nska and related to works of Wi\'sniewski, Sturmfels, Xu, Manon, Jeffrey, Weitsmann. 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.

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