Every connected graph with n≥7 vertices and at most floor(3n/2) edges has an independent minimum vertex cut; every connected graph with n≥7 and at most 2n edges has a foresty minimum vertex cut; both bounds are sharp.
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Sparse graphs with an independent or foresty minimum vertex cut
Every connected graph with n≥7 vertices and at most floor(3n/2) edges has an independent minimum vertex cut; every connected graph with n≥7 and at most 2n edges has a foresty minimum vertex cut; both bounds are sharp.