On Generalization of Cycles and Chordality to Clutters from an Algebraic Viewpoint

In this paper, we study the notion of chordality and cycles in clutters from a commutative algebraic point of view. The corresponding concept of chordality in commutative algebra is having a linear resolution. We mainly consider the generalization of chordality proposed by Bigdeli et al. in 2017 and the concept of cycles introduced by Cannon and Faridi in 2013, and study their interrelations and algebraic interpretations. In particular, we investigate the relationship between chordality and having linear quotients in some classes of clutters. Also, we show that if C is a clutter such that < C > is a vertex decomposable simplicial complex or I((C) over bar) is squarefree stable, then C is chordal.