In a recent work, Fouli and Lin generalized Villarreal's result and showed that if each connected component 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.
"On a class of squarefree monomial ideals of linear type." J. Commut. Algebra 7 (1) 125 - 140, SPRING 2015. https://doi.org/10.1216/JCA-2015-7-1-125