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

Authors: Jürgen Herzog, Takayuki Hibi, Ngô Viêt Trung and Xinxian Zheng
Journal: Trans. Amer. Math. Soc. 360 (2008), 6231-6249
MSC (2000): Primary 13A30, 05C65
DOI: https://doi.org/10.1090/S0002-9947-08-04461-9
Published electronically: July 28, 2008
MathSciNet review: 2434285
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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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