Edge ideals of oriented graphs

Huy Tài Ha; Kuei Nuan Lin; Susan Morey; Enrique Reyes; Rafael H. Villarreal

doi:10.1142/S0218196719500139

Edge ideals of oriented graphs

Huy Tài Ha, Kuei Nuan Lin, Susan Morey, Enrique Reyes, Rafael H. Villarreal

Penn State Greater Allegheny

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

27 Scopus citations

Abstract

Let be a weighted oriented graph and let I() be its edge ideal. Under a natural condition that the underlying (undirected) graph of contains a perfect matching consisting of leaves, we provide several equivalent conditions for the Cohen-Macaulayness of I(). We also completely characterize the Cohen-Macaulayness of I() when the underlying graph of is a bipartite graph. When I() fails to be Cohen-Macaulay, we give an instance where I() is shown to be sequentially Cohen-Macaulay.

Original language	English (US)
Pages (from-to)	535-559
Number of pages	25
Journal	International Journal of Algebra and Computation
Volume	29
Issue number	3
DOIs	https://doi.org/10.1142/S0218196719500139
State	Published - May 1 2019

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1142/S0218196719500139

Cite this

@article{b1aacdef3dd4403990da1dd973def533,

title = "Edge ideals of oriented graphs",

abstract = "Let be a weighted oriented graph and let I() be its edge ideal. Under a natural condition that the underlying (undirected) graph of contains a perfect matching consisting of leaves, we provide several equivalent conditions for the Cohen-Macaulayness of I(). We also completely characterize the Cohen-Macaulayness of I() when the underlying graph of is a bipartite graph. When I() fails to be Cohen-Macaulay, we give an instance where I() is shown to be sequentially Cohen-Macaulay.",

author = "Ha, {Huy T{\`a}i} and Lin, {Kuei Nuan} and Susan Morey and Enrique Reyes and Villarreal, {Rafael H.}",

note = "Publisher Copyright: {\textcopyright} 2019 World Scientific Publishing Company.",

year = "2019",

month = may,

day = "1",

doi = "10.1142/S0218196719500139",

language = "English (US)",

volume = "29",

pages = "535--559",

journal = "International Journal of Algebra and Computation",

issn = "0218-1967",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "3",

}

TY - JOUR

T1 - Edge ideals of oriented graphs

AU - Ha, Huy Tài

AU - Lin, Kuei Nuan

AU - Morey, Susan

AU - Reyes, Enrique

AU - Villarreal, Rafael H.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - Let be a weighted oriented graph and let I() be its edge ideal. Under a natural condition that the underlying (undirected) graph of contains a perfect matching consisting of leaves, we provide several equivalent conditions for the Cohen-Macaulayness of I(). We also completely characterize the Cohen-Macaulayness of I() when the underlying graph of is a bipartite graph. When I() fails to be Cohen-Macaulay, we give an instance where I() is shown to be sequentially Cohen-Macaulay.

AB - Let be a weighted oriented graph and let I() be its edge ideal. Under a natural condition that the underlying (undirected) graph of contains a perfect matching consisting of leaves, we provide several equivalent conditions for the Cohen-Macaulayness of I(). We also completely characterize the Cohen-Macaulayness of I() when the underlying graph of is a bipartite graph. When I() fails to be Cohen-Macaulay, we give an instance where I() is shown to be sequentially Cohen-Macaulay.

UR - http://www.scopus.com/inward/record.url?scp=85058823367&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85058823367&partnerID=8YFLogxK

U2 - 10.1142/S0218196719500139

DO - 10.1142/S0218196719500139

M3 - Article

AN - SCOPUS:85058823367

SN - 0218-1967

VL - 29

SP - 535

EP - 559

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 3

ER -

Edge ideals of oriented graphs

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this