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

preview_player
Показать описание
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!

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

********************************************************************
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.

********************************************************************

+WRATH OF MATH+

Follow Wrath of Math on...

Рекомендации по теме
Комментарии
Автор

Support the production of this course by joining Wrath of Math as a Channel Member for exclusive and early videos, original music, and upcoming lecture notes for the graph theory series! Plus your comments will be highlighted for me so it is more likely I'll answer your questions!

WrathofMath
Автор

Thank you for this great proof, you're a lifesaver!

vacannot
Автор

Thank you very much for this simple yet very well explained proof! I found this video very useful :)

mojo
Автор

Osm explanation
Love from India sir ❤

AnkitKumar-dgxr
Автор

can you please explain why n has to be odd? 3:30

tamiruzan
Автор

This one was little hard, glad i could understand it after watching couple of times and looking at other websites.

LearningCS-jpcb
Автор

Thank you so much for this video, you made it so simple !

RRatedT
Автор

Hello thanks for the nice explanation on this, please can you explain how odd cycle and even cycle relate with lattices?

evelinankayamba
Автор

If we If we assume that there is an odd circle in the graph, when we return to the initial vertex (V1) we have completed an odd circle (right?), then how can it be that Vn (the vertex before we closed a circle) will also be odd?

ElemenTalParkour
Автор

is this the same with complete bipartite graphs? Can they have no odd-length cycles?

p.s. love the video!

rainily
Автор

Prove that every diagraph without odd cycles has 1 basis .
What's Solution?

bhinisahu
Автор

Thanku sir... Do you have whatsapp sir?

yeezyeez
Автор

Thank you so much for explaining in such a wonderful way... presentation is much much better than the theory part.

rajashreedabre
Автор

does this proof also apply to the statement " a graph is bipartite if and only if every circuit in the graph has even length"?

shinelee
Автор

Can you please prove this with an example??

TmbuU
Автор

No odd cycles? More like "Nice lectures with which you bless us!" 🙏

PunmasterSTP