Regularity of edge ideal of a graph

TL;DR

This paper explores how certain graph reduction techniques preserve the regularity of edge ideals, providing an alternative proof for Fr"oberg's theorem on linear resolutions of graph edge ideals.

Contribution

It introduces graph reduction processes that maintain regularity and offers a new proof of Fr"oberg's theorem on linear resolutions.

Findings

Graph reductions preserve edge ideal regularity.

Alternative proof of Fr"oberg's theorem.

Enhanced understanding of edge ideal resolutions.

Abstract

In this paper, we introduce some reduction processes on graphs which preserve the regularity of related edge ideals. As a consequence, an alternative proof for the theorem of R. Fr\"oberg on linearity of resolution of edge ideal of graphs is given.