A CLASS OF HYPERGRAPHS THAT GENERALIZES CHORDAL GRAPHS

By E. Emtander. 2008

62 citations recorded by the source corpus.

In this paper we introduce a class of hypergraphs that we call chordal. We also extend the definition of triangulated hypergraphs, given by H. T. Ha and A. Van Tuyl, so that a triangulated hypergraph, according to our definition, is a natural generalization of a chordal (rigid circuit) graph. R. Froberg has showed that the chordal graphs corresponds to graph algebras, $R/I(\mathcal{G})$, with linear resolutions. We extend Froberg'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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/98f2182a127bc6dd750787a8d50a69344e2ce577

How researchers see this paper

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In Algebra and Number Theory

1. Adam Van Tuyl
2. Rafael H. Villarreal
3. Susan Morey
4. K. Kimura
5. Huy Tài Hà
6. Arindam Banerjee
7. Jürgen Herzog
8. Russ Woodroofe

In Computational Theory and Mathematics

1. Adam Van Tuyl
2. Rafael H. Villarreal
3. Susan Morey
4. K. Kimura
5. Huy Tài Hà
6. Jürgen Herzog
7. Arindam Banerjee

Citations in the corpus

• Edge ideals: algebraic and combinatorial properties (2010, background): “Much work has been done toward finding hypergraph generalizations of chordal graphs, typically by looking at cycles of edges or at tree hypergraphs [32, 53, 113].”
• A Beginner’s Guide to Edge and Cover Ideals (2013, background): “See [20, 32, 67] for some known facts about this case.”