Proof: Bipartite Graphs have no Odd Cycles | Graph Theory, Bipartite Theorem, Proofs

If a graph is bipartite then it has no odd cycles. This fact seems like it might not be obvious at first, but with a little bit of drawing and thinking, we can quickly demonstrate this result! In today's video graph theory lesson, we actually present two proofs of this result. The second proof uses contradiction, a favorite of mine! We'll be using the definition of bipartite graphs, and the definition of cycle, and it will lead us to our solution!

Quite interestingly, the converse of this statement is also true, that is "If a graph has no odd cycles, then it is bipartite" is also true. This is a much trickier statement to prove, and is much less obvious, even after some thinking and observation. I have a video lesson on a proof of this statement as well, if you are interested:    • Proof: If a Graph has no Odd Cycles t...  


I hope you find this video helpful, and be sure to ask any questions down in the comments!

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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.

Vallow Bandcamp: https://vallow.bandcamp.com/
Vallow Spotify: https://open.spotify.com/artist/0fRtu...
Vallow SoundCloud:   / benwatts-3  
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