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 |
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Pages (from-to) | 4249-4257 |
Number of pages | 9 |
Journal | Communications in Algebra |
Volume | 49 |
Issue number | 10 |
DOIs | |
Publication status | Published - 2021 |
Keywords
- Cohen-Macaulay graph
- edge-weighted graph
- unmixed ideal
- weighted edge ideal
ASJC Scopus subject areas
- Algebra and Number Theory