Proof: Closed Odd Walk contains Odd Cycle | Graph Theory

We prove that a closed odd walk contains an odd cycle. This result is also part of the proof that a graph is bipartite if and only if it contains no odd cycles, so it's important! The argument has to do with the fact that an odd closed walk can be broken down into cycles, and one of these cycles must be odd for the whole walk to be odd. #GraphTheory

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[WrathofMath]

Feels good to be making graph theory content again! Continuing to grow the playlist, currently 156 videos strong. There is much left to cover!

[plasmacrab_]

Very neat proof! I never learned about graph theory aside from the basics, but your explanation was very intuitive that (I think) I understand the entire proof. Thanks for the quality video! I'll definitely be watching more of your graph theory.

[praveenkumarp]

your channel is underrated. great work man

[ibnuahmedbare]

wooow. it 1:48am i am reviewing for my final exam and I found myself clapping when you finished the proof wow

[huiwencheng]

The best proof for this lemma I have ever seen!!

[gordgodgord]

You should also be careful, it may be more than 2 v-v walks and since the *sum of some even numbers is even* and the length of W is odd then at least one of these v-v walks should be odd otherwise then l is even by the *(bold sentence) which is not.

[PunmasterSTP]

The proof makes sense, but things still seem just a bit...odd.