Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs
classification
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math.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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