A class of hypergraphs that generalizes chordal graphs
Commutative Algebra
2008-03-28 v2 Combinatorics
Abstract
In this paper we introduce a class of hypergraphs that we call chordal. We also extend the definition of triangulated hypergraphs, given in \cite{VT}, so that a triangulated hypergraph, according to our definition, is a natural generalization of a chordal (rigid circuit) graph. In \cite{F1}, Fr\"oberg shows that the chordal graphs corresponds to graph algebras, , with linear resolutions. We extend Fr\"oberg's method and show that the hypergraph algebras of generalized chordal hypergraphs, a class of hypergraphs that includes the chordal hypergraphs, have linear resolutions. The definitions we give, yield a natural higher dimensional version of the well known flag property of simplicial complexes. We obtain what we call -flag complexes.
Cite
@article{arxiv.0803.2150,
title = {A class of hypergraphs that generalizes chordal graphs},
author = {Eric Emtander},
journal= {arXiv preprint arXiv:0803.2150},
year = {2008}
}