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 journalArticlepeer-review

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 languageEnglish
Pages (from-to)4249-4257
Number of pages9
JournalCommunications in Algebra
Volume49
Issue number10
DOIs
Publication statusPublished - 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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