Hamilton Circuits: Ore's Theorem (Statement and Proof)

[@csuklashablaty671]

he jjust read the wikipedia.

[@evandoyle8389]

Deriving the final inequality (deg(u) + deg(v)

[@IqbalShahid]

Thank you for the kind words. I am glad I was able to contribute.

[@TheZ10Z]

Direct to the point.

[@IqbalShahid]

Thank you

[@corporalwaffles]

At 5:40, can you explain why do we subtract deg(u) from the inequality?

[@IqbalShahid]

Thank you for the comment.
The build-up of this statement was that for each node that is adjacent to u, there is a corresponding node that cannot be adjacent to v. Since there are deg(u) such nodes, we have deg(u) more nodes that are not adjacent to v. Hope it helps.

[@mrityunjoynath3995]

Elegant one . Thanks you should continue making them.

[@IqbalShahid]

+Mrityunjoy Nath Thank you for the motivational message! Appreciate it very much.

[@asthapandey8068]

Thanks for such a simple but awesome proof :)

[@IqbalShahid]

Thank you for the kind words of appreciation!

[@tripatisahu1722]

Thank you

[@IqbalShahid]

Thank you for the words of appreciation.

[@אוראלבןשמאי]

Thank you very much!

[@GokulNathXYZ]

Wonderful, thanks a lot.

[@IqbalShahid]

Thank you for your interest and kind words.

[@radicalpotato666]

Thanks!

[@IqbalShahid]

Thank you

[@joshua_dlima]

thanks a tonne!

[@IqbalShahid]

Thank you for the kind words

[@sriharshaananthoju8671]

But you have proved only if G is maximal non Hamiltonian case

[@IqbalShahid]

Thank you for the comment. G can be any simple graph satisfying the condition of the theorem. The maximal non Hamiltonian graph is constructed to facilitate the outline of the proof. Hope it helps.