Edge rings with $q$-linear resolutions

Abstract

In the present paper, we give a complete classification of connected simple graphs whose edge rings have a $q$-linear resolution with $q\ge 2$. In particular, we show that the edge ring of a finite connected simple graph with a $q$-linear resolution, where $q\ge 3$, is a hypersurface, which was conjectured by Hibi, Matsuda, and Tsuchiya.

18 pages, 7 figures

References in corpus (2)

• Edge rings with $3$-linear resolutions
• Edge rings of bipartite graphs with linear resolutions