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Proceedings of the American Mathematical Society

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Vertex cover algebras of unimodular hypergraphs

Authors: Jürgen Herzog, Takayuki Hibi and Ngô Viêt Trung
Journal: Proc. Amer. Math. Soc. 137 (2009), 409-414
MSC (2000): Primary 13D02, 05C65
Published electronically: October 9, 2008
MathSciNet review: 2448558
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Abstract: It is proved that all vertex cover algebras of a hypergraph are standard graded if and only if the hypergraph is unimodular. This has interesting consequences on the symbolic powers of monomial ideals.

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Additional Information

Jürgen Herzog
Affiliation: Fachbereich Mathematik und Informatik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany
MR Author ID: 189999

Takayuki Hibi
Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan
MR Author ID: 219759

Ngô Viêt Trung
Affiliation: Institute of Mathematics, Vien Toan Hoc, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam
MR Author ID: 207806

Keywords: Vertex cover algebra, unimodular hypergraph, symbolic power, monomial ideal
Received by editor(s): March 18, 2007
Published electronically: October 9, 2008
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2008 American Mathematical Society