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

34 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

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10.1142/S0218196719500139

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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.",

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AU - Morey, Susan

AU - Reyes, Enrique

AU - Villarreal, Rafael H.

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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.

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ER -

Edge ideals of oriented graphs

Abstract

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