Lovász-Saks-Schrijver ideals and parity binomial edge ideals of graphs

Abstract

Let $G$ be a simple graph on $n$ vertices. Let $L_G\text{ and }{\mathcal{I}}_G$ denote the Lovász-Saks-Schrijver(LSS) ideal and parity binomial edge ideal of $G$ in the polynomial ring $S=\mathbb{K}[x_1,\dots ,x_n,y_1,\dots ,y_n]$ respectively. We classify graphs whose LSS ideals and parity binomial edge ideals are complete intersections. We also classify graphs whose LSS ideals and parity binomial edge ideals are almost complete intersections, and we prove that their Rees algebra is Cohen-Macaulay. We compute the second graded Betti number and obtain a minimal presentation of LSS ideals of trees and odd unicyclic graphs. We also obtain an explicit description of the defining ideal of the symmetric algebra of LSS ideals of trees and odd unicyclic graphs.

22 pages, Accepted for publication in European J. Combin

References in corpus (1)

• Binomial edge ideals and bounds for their regularity

Cited by in corpus (1)

• Regularity of powers of d-sequence (parity) binomial edge ideals of unicycle graphs