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Let G be a connected graph and let $I(G)$ denote its edge ideal. We classify when I(G)ⁿ, for n ≥ 1, admits a minimal Lyubeznik resolution. We also give a characterization for when I(G)ⁿ is bridge-friendly, which, in turn, implies that I(G)ⁿ has a minimal Barile-Macchia cellular resolution.
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Chau et al. (2024) studied this question.
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