Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs

Seyed Amin Seyed Fakhari; Kosuke Shibata; Naoki Terai; Siamak Yassemi

doi:10.1080/00927872.2021.1917590

Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs

Seyed Amin Seyed Fakhari, Kosuke Shibata, Naoki Terai, Siamak Yassemi

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

1 Citation (Scopus)

Abstract

We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. We also provide examples of oriented graphs that have unmixed and non-Cohen-Macaulay vertex-weighted edge ideals, while the edge ideal of their underlying graph is Cohen-Macaulay. This disproves a conjecture posed by Pitones, Reyes, and Toledo.

Original language	English
Pages (from-to)	4249-4257
Number of pages	9
Journal	Communications in Algebra
Volume	49
Issue number	10
DOIs	https://doi.org/10.1080/00927872.2021.1917590
Publication status	Published - 2021

Keywords

Cohen-Macaulay graph
edge-weighted graph
unmixed ideal
weighted edge ideal

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2021.1917590

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title = "Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs",

abstract = "We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. We also provide examples of oriented graphs that have unmixed and non-Cohen-Macaulay vertex-weighted edge ideals, while the edge ideal of their underlying graph is Cohen-Macaulay. This disproves a conjecture posed by Pitones, Reyes, and Toledo.",

keywords = "Cohen-Macaulay graph, edge-weighted graph, unmixed ideal, weighted edge ideal",

author = "{Seyed Fakhari}, {Seyed Amin} and Kosuke Shibata and Naoki Terai and Siamak Yassemi",

note = "Funding Information: This work was partially supported by JSPS Grant-in-Aid for Scientific Research (C) 18K03244. We thank the anonymous referee for careful reading and valuable comments. Publisher Copyright: {\textcopyright} 2021 Taylor & Francis Group, LLC.",

year = "2021",

doi = "10.1080/00927872.2021.1917590",

language = "English",

volume = "49",

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T1 - Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs

AU - Seyed Fakhari, Seyed Amin

AU - Shibata, Kosuke

AU - Terai, Naoki

AU - Yassemi, Siamak

N1 - Funding Information: This work was partially supported by JSPS Grant-in-Aid for Scientific Research (C) 18K03244. We thank the anonymous referee for careful reading and valuable comments. Publisher Copyright: © 2021 Taylor & Francis Group, LLC.

PY - 2021

Y1 - 2021

N2 - We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. We also provide examples of oriented graphs that have unmixed and non-Cohen-Macaulay vertex-weighted edge ideals, while the edge ideal of their underlying graph is Cohen-Macaulay. This disproves a conjecture posed by Pitones, Reyes, and Toledo.

AB - We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. We also provide examples of oriented graphs that have unmixed and non-Cohen-Macaulay vertex-weighted edge ideals, while the edge ideal of their underlying graph is Cohen-Macaulay. This disproves a conjecture posed by Pitones, Reyes, and Toledo.

KW - Cohen-Macaulay graph

KW - edge-weighted graph

KW - unmixed ideal

KW - weighted edge ideal

UR - http://www.scopus.com/inward/record.url?scp=85105138720&partnerID=8YFLogxK

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DO - 10.1080/00927872.2021.1917590

M3 - Article

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VL - 49

SP - 4249

EP - 4257

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 10

ER -

Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs

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Keywords

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