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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.
Chau et al. (Fri,) studied this question.