Standard graded vertex cover algebras, cycles and leaves

Herzog, Jürgen; Hibi, Takayuki; Trung, Ngô; Zheng, Xinxian

doi:10.1090/S0002-9947-08-04461-9

Standard graded vertex cover algebras, cycles and leaves
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by Jürgen Herzog, Takayuki Hibi, Ngô Viêt Trung and Xinxian Zheng PDF

Trans. Amer. Math. Soc. 360 (2008), 6231-6249 Request permission

Abstract:

The aim of this paper is to characterize simplicial complexes which have standard graded vertex cover algebras. This property has several nice consequences for the squarefree monomial ideals defining these algebras. It turns out that such simplicial complexes are closely related to a range of hypergraphs which generalize bipartite graphs and trees. These relationships allow us to obtain very general results on standard graded vertex cover algebras which cover previous major results on Rees algebras of squarefree monomial ideals.

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