Question: Let G be a connected graph with a cut {X, Y} with G[X] (the subgraph of G on the node set ) connected but

Let G be a connected graph with a cut {X, Y} with

Let G be a connected graph with a cut {X, Y} with G[X] (the subgraph of G on the node set ) connected but G[Y] disconnected, with exactly two components G[Y1] and G[Y2]. Prove or disprove: (X,Y) is a min cut of G.

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