Gorenstein binomial edge ideals associated with scrolls

TL;DR

This paper characterizes graphs for which the associated binomial edge ideals are Gorenstein and have maximal regularity, focusing on the algebraic properties linked to the structure of the graph.

Contribution

It provides a complete characterization of graphs G where the binomial edge ideal I_G is Gorenstein and has maximal regularity, connecting graph theory with algebraic properties.

Findings

Identifies graphs with Gorenstein binomial edge ideals.

Determines conditions for maximal regularity of I_G.

Establishes a link between graph structure and algebraic properties.

Abstract

Let $I_G$ be the binomial edge ideal on the generic 2 x n - Hankel matrix associated with a closed graph $G$ on the vertex set [n]. We characterize the graphs $G$ for which $I_G$ has maximal regularity and is Gorenstein.