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

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arxiv 2003.12379 v1 pith:VZNH2NTQ submitted 2020-03-27 math.AC math.CO

Seyed Amin Seyed Fakhari , Kosuke Shibata , Naoki Terai , Siamak Yassemi This is my paper · ORCID
classification math.ACmath.CO
keywords edgecohen-macaulaygraphsidealsedge-weightedunmixedverywell-covered
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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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