Journal of Algebraic Combinatorics

, Volume 35, Issue 3, pp 421–460

Phylogenetic toric varieties on graphs

Open AccessArticle

DOI: 10.1007/s10801-011-0308-2

Cite this article as:
Buczyńska, W. J Algebr Comb (2012) 35: 421. doi:10.1007/s10801-011-0308-2


We define phylogenetic projective toric model of a trivalent graph as a generalization of a binary symmetric model of a trivalent phylogenetic tree. Generators of the projective coordinate ring of the models of graphs with one cycle are explicitly described. The phylogenetic models of graphs with the same topological invariants are deformation-equivalent and share the same Hilbert function. We also provide an algorithm to compute the Hilbert function.


Binary symmetric modelGIT quotientHilbert function
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© The Author(s) 2011

Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA