Edge rings with $3$-linear resolutions
Takayuki Hibi, Kazunori Matsuda, Akiyoshi Tsuchiya
TL;DR
This paper proves that the edge ring of a finite connected simple graph with a 3-linear resolution must be a hypersurface, revealing a specific geometric property linked to algebraic resolution conditions.
Contribution
The paper establishes a new characterization of edge rings with 3-linear resolutions, showing they are hypersurfaces, which was not previously known.
Findings
Edge rings with 3-linear resolutions are hypersurfaces
Connectedness of the graph is a key condition
Provides a geometric-algebraic link in graph theory
Abstract
It is shown that the edge ring of a finite connected simple graph with a -linear resolution is a hypersurface.
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