Geodesic
Some algebraic properties of hypergraphs
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 577-607.

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We consider Stanley-Reisner rings $k[x_1,\ldots ,x_n]/I(\mathcal {H})$ where $I(\mathcal {H})$ is the edge ideal associated to some particular classes of hypergraphs. For instance, we consider hypergraphs that are natural generalizations of graphs that are lines and cycles, and for these we compute the Betti numbers. We also generalize some known results about chordal graphs and study a weak form of shellability.
DOI : 10.1007/s10587-011-0031-0
Classification : 05C25, 05C40, 05C65, 05C75, 13D02, 13F20, 13H10
Keywords: Betti numbers; chordal hypergraphs; connectivity; homologically connected hypergraphs; hypercycles; line hypergraphs; shellability 
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Emtander, Eric; Mohammadi, Fatemeh; Moradi, Somayeh. Some algebraic properties of hypergraphs. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 577-607. doi : 10.1007/s10587-011-0031-0. http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0031-0/

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