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

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.

preprint2020arXivOpen access
Seyed Amin Seyed FakhariKosuke ShibataNaoki TeraiSiamak Yassemi
math.COmath.AC
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Open access4 authors2 topics
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Seyed Amin Seyed FakhariKosuke ShibataNaoki TeraiSiamak Yassemi

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