Why did the author assume there exist three connected components for $G\setminus u$?. In the statement of the theorem, it is not given. Can you explain why did the author use the underlined statement?
2026-04-01 13:17:08.1775049428
Why did the author assume there exist three connected components for $G\setminus u$?
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The drawing has three components, but the wording of the proof only assumes there are at least two (one containing $v$, and at least one not containing $v$). There are at least two because we've assumed (for contradiction) that $u$ is a cut vertex, and that's what "cut vertex" means.