Algebraic properties of toric rings of graphs

Abstract

Let $G = (V,E)$ be a simple graph. We investigate the Cohen-Macaulayness and algebraic invariants, such as the Castelnuovo-Mumford regularity and the projective dimension, of the toric ring $k[G]$ via those of toric rings associated to induced subgraphs of $G$.Comment: 18 pages; changed title and re-organized sections to better exhibit results; correct the last main theore