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A class of hypergraphs that generalizes chordal graphs

Authors
  • Emtander, Eric
Type
Preprint
Publication Date
Mar 28, 2008
Submission Date
Mar 14, 2008
Identifiers
arXiv ID: 0803.2150
Source
arXiv
License
Yellow
External links

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, $R/I(\mc{G})$, 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 $d$-flag complexes.

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