  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.
