Robust Graph Ideals
Combinatorics
2013-10-01 v1 Commutative Algebra
Abstract
Let I be a toric ideal. We say I is robust if its universal Groebner basis is a minimal generating set. We show that any robust toric ideal arising from a graph G is also minimally generated by its Graver basis. We then completely characterize all graphs which give rise to robust ideals. Our characterization shows that robustness can be determined solely in terms of graph-theoretic conditions on the set of circuits of G.
Cite
@article{arxiv.1309.7630,
title = {Robust Graph Ideals},
author = {Adam Boocher and Bryan Christopher Brown and Timothy Duff and Laura Lyman and Takumi Murayama and Amy Nesky and Karl Schaefer},
journal= {arXiv preprint arXiv:1309.7630},
year = {2013}
}
Comments
16 pages, 9 figures