Regularity and h-polynomials of toric ideals of graphs
- Autori: Favacchio G.; Keiper G.; Tuyl A.V.
- Anno di pubblicazione: 2020
- Tipologia: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/534011
Abstract
For all integers 4 ≤ r ≤ d, we show that there exists a finite simple graph G = Gr,d with toric ideal IG ⊂ R such that R/IG has (Castelnuovo-Mumford) regularity r and h-polynomial of degree d. To achieve this goal, we identify a family of graphs such that the graded Betti numbers of the associated toric ideal agree with its initial ideal, and, furthermore, that this initial ideal has linear quotients. As a corollary, we can recover a result of Hibi, Higashitani, Kimura, and O'Keefe that compares the depth and dimension of toric ideals of graphs.