Edge rings of bipartite graphs with linear resolutions

Abstract

Ohsugi and Hibi characterized the edge ring of a finite connected simple graph with a $2$-linear resolution. On the other hand, Hibi, Matsuda and the author conjectured that the edge ring of a finite connected simple graph with a $q$-linear resolution, where $q\ge 3$, is a hypersurface and proved the case $q=3$. In the present paper, we solve this conjecture for the case of finite connected simple bipartite graphs.

8 pages. arXiv admin note: text overlap with arXiv:1712.03504

References in corpus (3)

• Root polytopes, Tutte polynomials, and a duality theorem for bipartite graphs
• Ehrhart Theory of Spanning Lattice Polytopes
• Edge rings with $3$-linear resolutions

Cited by in corpus (1)

• Edge rings with $q$-linear resolutions