2008/03/14 by Eric Emtander, Emtander, Eric · 1 citation
Mathematics · #05C65 #13D02 #13D07 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CO #msc:05C65 #msc:13D02 #msc:13D07
paper · pdf · doi:10.48550/arxiv.0803.2150
arxiv created 2008/03/28 · arxiv updated 2009/12/01
In this paper we introduce a class of hypergraphs that we call chordal. We also extend the definition of triangulated hypergraphs, given in \citeVT, so that a triangulated hypergraph, according to our definition, is a natural generalization of a chordal (rigid circuit) graph. In \citeF1, Fröberg shows that the chordal graphs corresponds to graph algebras, R/I(\mcG), with linear resolutions. We extend Fröberg'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.