Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs
Commutative Algebra
2020-03-30 v1 Combinatorics
Abstract
We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. We also provide examples of oriented graphs which 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
Cite
@article{arxiv.2003.12379,
title = {Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs},
author = {Seyed Amin Seyed Fakhari and Kosuke Shibata and Naoki Terai and Siamak Yassemi},
journal= {arXiv preprint arXiv:2003.12379},
year = {2020}
}