On a class of squarefree monomial ideals of linear type

TL;DR

This paper revisits and simplifies a known criterion for squarefree monomial ideals to be of linear type, and introduces a new class of such ideals.

Contribution

It provides a new proof of a recent result and proposes a novel class of squarefree monomial ideals of linear type.

Findings

Reproved a recent criterion for linear type ideals using original and new methods.

Proposed a new class of squarefree monomial ideals of linear type.

Abstract

In a recent work, Fouli and Lin generalized a Villarreal's result and showed that if each connected components of the line graph of a squarefree monomial ideal contains at most a unique odd cycle, then this ideal is of linear type. In this short note, we reprove this result with Villarreal's original ideas together with a method of Conca and De Negri. We also propose a class of squarefree monomial ideals of linear type.