On Generalizations of Cycles and Chordality to Hypergraphs

Ashkan Nikseresht, Rashid Zaare-Nahandi

Published 2016-01-13Version 1

In this paper, we study the notion of chordality and cycles in hypergraphs with a commutative algebraic point of view. The corresponding concept of chordality in commutative algebra is having a linear resolution. However, there is not unified definition for cycle or chordality in hypergraphs in the literature, we consider several generalizations of these notions and study their algebraic interpretations. In particular, we investigate the relationship between chordality and having linear quotients in some classes of hypergraphs. Also we show that if $\mathcal{C}$ is a hypergraph such that $\langle \mathcal{C} \rangle$ is a vertex decomposable simplicial complex or $I(\bar{\mathcal{C}})$ is squarefree stable, then $\mathcal{C}$ is chordal according to one of the most promising definitions.