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The Bottleneck Lemma states that if a bipartite graph has a bottleneck, then no perfect matching exists. This is considered obvious from the counting argument.

Conditions: There is a subset S of the left-side vertices.; |S| > |$E(S)$|.

The Bottleneck Lemma states that if a bipartite graph has a bottleneck, then no perfect matching exists. This is considered obvious from the counting argument.

Conditions: There is a subset S of the left-side vertices.; |S| > |$E(S)$|.