Unmixed graphs that are domains

Bruno Benedetti; Matteo Varbaro

doi:10.1080/00927872.2010.519363

Unmixed graphs that are domains

Bruno Benedetti, Matteo Varbaro

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We extend a theorem of Villareal on bipartite graphs to the class of all graphs. On the way to this result, we study the basic covers algebra Ā(G) of an arbitrary graph G. We characterize with purely combinatorial methods the cases when 1) Ā(G) is a domain and 2) G is unmixed and Ā(G) is a domain.

Original language	English (US)
Pages (from-to)	2260-2267
Number of pages	8
Journal	Communications in Algebra
Volume	39
Issue number	7
DOIs	https://doi.org/10.1080/00927872.2010.519363
State	Published - Jul 2011
Externally published	Yes

Keywords

Basic covers
Minimal vertex covers
Symbolic powers
Unmixed graphs

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2010.519363

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abstract = "We extend a theorem of Villareal on bipartite graphs to the class of all graphs. On the way to this result, we study the basic covers algebra Ā(G) of an arbitrary graph G. We characterize with purely combinatorial methods the cases when 1) Ā(G) is a domain and 2) G is unmixed and Ā(G) is a domain.",

keywords = "Basic covers, Minimal vertex covers, Symbolic powers, Unmixed graphs",

author = "Bruno Benedetti and Matteo Varbaro",

note = "Funding Information: We would like to thank Aldo Conca and J{\"u}rgen Herzog for the kind support and encouragement. The first author was supported by DFG via the Berlin Mathematical School. Copyright: Copyright 2011 Elsevier B.V., All rights reserved.",

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AU - Benedetti, Bruno

AU - Varbaro, Matteo

N1 - Funding Information: We would like to thank Aldo Conca and Jürgen Herzog for the kind support and encouragement. The first author was supported by DFG via the Berlin Mathematical School. Copyright: Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/7

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N2 - We extend a theorem of Villareal on bipartite graphs to the class of all graphs. On the way to this result, we study the basic covers algebra Ā(G) of an arbitrary graph G. We characterize with purely combinatorial methods the cases when 1) Ā(G) is a domain and 2) G is unmixed and Ā(G) is a domain.

AB - We extend a theorem of Villareal on bipartite graphs to the class of all graphs. On the way to this result, we study the basic covers algebra Ā(G) of an arbitrary graph G. We characterize with purely combinatorial methods the cases when 1) Ā(G) is a domain and 2) G is unmixed and Ā(G) is a domain.

KW - Basic covers

KW - Minimal vertex covers

KW - Symbolic powers

KW - Unmixed graphs

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JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 7

ER -

Unmixed graphs that are domains

Abstract

Keywords

ASJC Scopus subject areas

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