Unmixed graphs that are domains

Bruno Benedetti, Matteo Varbaro

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)2260-2267
Number of pages8
JournalCommunications in Algebra
Volume39
Issue number7
DOIs
StatePublished - Jul 2011
Externally publishedYes

Fingerprint

Graph in graph theory
Bipartite Graph
Cover
Algebra
Arbitrary
Theorem
Class

Keywords

  • Basic covers
  • Minimal vertex covers
  • Symbolic powers
  • Unmixed graphs

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Unmixed graphs that are domains. / Benedetti, Bruno; Varbaro, Matteo.

In: Communications in Algebra, Vol. 39, No. 7, 07.2011, p. 2260-2267.

Research output: Contribution to journalArticle

Benedetti, Bruno ; Varbaro, Matteo. / Unmixed graphs that are domains. In: Communications in Algebra. 2011 ; Vol. 39, No. 7. pp. 2260-2267.
@article{5408ec7b569c4fa2b8cdf9e4aab3a62f,
title = "Unmixed graphs that are domains",
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",
year = "2011",
month = "7",
doi = "10.1080/00927872.2010.519363",
language = "English (US)",
volume = "39",
pages = "2260--2267",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",
number = "7",

}

TY - JOUR

T1 - Unmixed graphs that are domains

AU - Benedetti, Bruno

AU - Varbaro, Matteo

PY - 2011/7

Y1 - 2011/7

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

UR - http://www.scopus.com/inward/record.url?scp=79960715351&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960715351&partnerID=8YFLogxK

U2 - 10.1080/00927872.2010.519363

DO - 10.1080/00927872.2010.519363

M3 - Article

AN - SCOPUS:79960715351

VL - 39

SP - 2260

EP - 2267

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 7

ER -