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arXiv · 2003.12379

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

Seyed Amin Seyed Fakhari·Kosuke Shibata·Naoki Terai·Siamak Yassemi
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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.

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Seyed Amin Seyed Fakhari, Kosuke Shibata, Naoki Terai, Siamak Yassemi. 2020-03-27. Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. https://arxiv.org/abs/2003.12379

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