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The example proves no matching is possible because the highlighted subset of three girls has a neighborhood of only two boys. Since |S| = $3 > 2$ = |$E(S)$|, this subset is a bottleneck, and by the Bottleneck Lemma, no matching can cover all girls.

Conditions: A bipartite graph with left set G and right set B.; A highlighted subset S of three girls.; Their collective neighborhood $E(S)$ contains only two boys.

The example proves no matching is possible because the highlighted subset of three girls has a neighborhood of only two boys. Since |S| = $3 > 2$ = |$E(S)$|, this subset is a bottleneck, and by the Bottleneck Lemma, no matching can cover all girls.

Conditions: A bipartite graph with left set G and right set B.; A highlighted subset S of three girls.; Their collective neighborhood $E(S)$ contains only two boys.