Abstract
Let 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.
Acknowledgements
Part of this work was done when the first two authors were visiting Vietnam Institute for Advanced Study in Mathematics (VIASM). The authors would like to thank VIASM for its support and hospitality. The authors would also like to thank K. Kimura for providing Example 5.4 and for spotting a gap in our first draft.