The incorrect proof of the Dirac's theorem about Hamiltonian graphs on ProofWiki

Episode 46.

The incorrect proof of the Dirac's theorem about Hamiltonian graphs on ProofWiki.

The statement of the Dirac's theorem on ProofWiki incorrectly assumes that the graph is connected and uses it in the last part of the proof.
https://proofwiki.org/wiki/Dirac%27s_Theorem

The correct statement of this theorem does not assume that the graph is connected and the proof should not use it. Of course, any Hamiltonian graph must be connected, so the connectedness of the graph satisfying the conditions of the theorem follows from the theorem as a conclusion, but it is a conclusion, not an assumption.

The main video about the Dirac's theorem:
https://youtu.be/7sNdIM4F5SI
https://rumble.com/v5be18p-diracs-theorem-about-hamiltonian-graphs-graph-theory.html
https://t.me/mathematical_bunker/68

Mathematics. Discrete Mathematics. Combinatorics. Graph theory.
#Mathematics #DiscreteMathematics #Combinatorics #GraphTheory

The same video on YouTube:
https://youtu.be/NNBxfiVLBqc

The same video on Telegram:
https://t.me/mathematical_bunker/70