Regularity bounds for binomial edge ideals

TL;DR

This paper establishes bounds on the Castelnuovo-Mumford regularity of binomial edge ideals based on graph properties, specifically relating to the longest induced path and total vertices.

Contribution

It provides new bounds on the regularity of binomial edge ideals, linking algebraic invariants to combinatorial graph parameters.

Findings

Regularity is at least the length of the longest induced path.

Regularity is at most the number of vertices in the graph.

Bounds connect algebraic and combinatorial graph properties.

Abstract

We show that the Castelnuovo-Mumford regularity of the binomial edge ideal of a graph is bounded below by the length of its longest induced path and bounded above by the number of its vertices.