How to Tell if Graph is Bipartite (by hand) | Graph Theory
How can we tell if a graph is bipartite by hand? We'll discuss the easiest way to identify bipartite graphs in today's graph theory lesson. This method takes advantage of the fact that bipartite graphs are 2-colorable. This means their vertices can be colored using only two colors so adjacent vertices are colored differently (sometimes called a proper coloring). You may easily see that being 2-colorable and bipartite are the exact same things! #GraphTheory
Since a graph being bipartite is the same as being 2-colorable, to determine if a graph is bipartite we simply pick a vertex v to begin coloring - then assign it Color 1. If the graph is bipartite, then the neighbors of v must be colored with Color 2. We continue in this way, coloring neighbors different colors (using only two colors total) until we either finish coloring the graph or we are forced to color two adjacent vertices the same way. If two adjacent vertices are forced to be colored the same way, then the graph cannot possibly be bipartite - since we have been forced to put adjacent vertices in the same set (or color). If we are able to finish coloring the graph - then it is bipartite and we now have a bipartite partitioning of the graph into two colored sets.
Bipartite Graphs: • What is a Bipartite Gr...
Proof Graph with no Odd Cycles is Bipartite: • Proof: If a Graph has ...
Vertex Colorings and Chromatic Numbers: • Vertex Colorings and t...
Graph Theory playlist: • Graph Theory
★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: / wrathofmathlessons
◆ Donate on PayPal: www.paypal.me/wrathofmath
Thanks to Robert Rennie, Barbara Sharrock, and Rolf Waefler for their generous support on Patreon!
Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: crayonangel.bandcamp.com/
Follow Wrath of Math on...
● Instagram: / wrathofmathedu
● Facebook: / wrathofmath
● Twitter: / wrathofmathedu
My Music Channel: / @emery3050
Пікірлер: 100
If you're into Graph Theory, check out my Graph Theory playlist, with more than 150 videos and more than 100,000 views! And many more of both to come! kzread.info/head/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH If you're enjoying the Christmas lessons, please share them around - it's a huge help!
Currently taking Discrete Math 2 and the textbook definition for Bipartite-ness was so verbose and hard to comprehend, but this made it so easy, thank you!!!!!
@WrathofMath
Жыл бұрын
So glad it helped!
@PunmasterSTP
Ай бұрын
I didn't even know Discrete Math could be divided up into multiple classes. What did you think of it, and did you have a favorite one?
Thanks we didnt learn this in discrete 2 at rutgers despite learning bipartite. They seem so anti visualization even when it'll obviously make things clearlier to many people.
@PunmasterSTP
Ай бұрын
Oh man, I'm sorry to hear that! I can't even think about approaching graph theory in a non-visual way.
Great job, my friend. Seen many of your videos, in particular the one that you prove Ore´s theorem. Merry Christmas to you! Greetings from Argentina!
Thanks for the explanation!!! Makes this concept clearer.
Great video such a clear explanation, thank you!
@WrathofMath
2 жыл бұрын
Thanks, Julianna, glad to help! Check out my playlist if you're looking for more, and let me know if you have any questions! kzread.info/head/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
Perfect explanation ,thank you
Super clear explanation! Thank you for making this. 🙂
@WrathofMath
2 жыл бұрын
My pleasure, glad it was clear! Let me know if you have any questions and check out my graph theory playlist for more! kzread.info/head/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
Perfectly explained, thank you so much!!
@WrathofMath
Жыл бұрын
Thank you for watching!
Perfect explanation. Very easy and clear. Thank you :)
@WrathofMath
2 жыл бұрын
So glad it was helpful! Thanks for watching and check out my graph theory playlist for more! kzread.info/head/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
Thank you, this video helped out a lot.
its sad that you only have 100k subscribers , you deserve millions !
@WrathofMath
4 ай бұрын
Thank you!
that's incredibly helpful! Thank you!!
@WrathofMath
2 жыл бұрын
My pleasure, glad you thought so!
Such a Great Explanation...Thank you so much...hope you will make more and more videos for us....😊😊😊
Thanks for a clear explanation. I love your christmas decorations!
@WrathofMath
8 ай бұрын
Thank you! Also, i don't know the origin of your name - but I am very pro-frog!
Good quick concise video that gets straight to the point for beginners. 👌🏼
@WrathofMath
Ай бұрын
Thanks for watching!
Very useful to save some time 😀 thanks for the video
Short, simple, amazing!
@WrathofMath
2 ай бұрын
Thank you!
god bless got me through homework questions that were taking me an hour to even start in a good 6 minutes. thank you!!!
@WrathofMath
6 ай бұрын
Glad it helped!
Always a life saver, thanks
@WrathofMath
2 жыл бұрын
Glad to help - thanks for watching!
Very helpful, thank you!
@WrathofMath
Жыл бұрын
That's what I like to hear, my pleasure!
Amazing , now i can identify any graph .Thank you so much . 😀
@WrathofMath
Жыл бұрын
Glad to help!
I watched a lot of your videos。 I love you🥰
Such a Great Explanation. Thank you :)
@WrathofMath
Жыл бұрын
Thank you for watching!
2 colorable? More like "2 good"...to us by making these outstanding lectures available for free!
Love from Philippines! Currently taking Discrete Math for my engineering course T_T. Definitions from my e-book made it seem borderline impossible to understand without visuals. I really found your video helpful, thank you!
@PunmasterSTP
Ай бұрын
Oh man, good luck in the course!
Thankyou, it was a very clear description :
@WrathofMath
9 ай бұрын
Thanks for watching!
Thank you!
I LOVE THIS TEACHER OMG
@WrathofMath
7 ай бұрын
Thank you!
one of the greatest faculty ever
Great video. Keep going 🙌
@WrathofMath
2 жыл бұрын
Thank you, I will! Let me know if you have any graph theory video requests!
Thanks a lot, good explanation.
@WrathofMath
Жыл бұрын
Glad to help, thanks for watching!
Beautiful
bless you brother
Awesome!!
Thank you sir 😍😍
Excellent video sir
@WrathofMath
7 ай бұрын
Many thanks!
Great video!
@WrathofMath
2 жыл бұрын
Thanks Micah!
Thank you Dear!
@WrathofMath
Жыл бұрын
Glad to help, thanks for watching!
Thanks a lot
@WrathofMath
Жыл бұрын
Glad to help!
I can’t think you enough 😢❤
god bless you mahn!!!!
YOU JUST SAVE MY LIFE
@WrathofMath
10 ай бұрын
Awesome! Thanks for watching!
thank you so much
@WrathofMath
Күн бұрын
Glad to help - thanks for watching!
thank you so so so so so soooooooooooo.....much
Man ! Thanks
@WrathofMath
2 жыл бұрын
My pleasure, thanks for watching and let me know if you ever have any graph theory video requests!
very good
@WrathofMath
Жыл бұрын
Thank you!
thanks bro
@WrathofMath
6 ай бұрын
Glad to help!
And what make a graph uniquely (1 way to 2 colore it) or not( 1+ ways to colore it) 2-colored ?
Very good explanation, thanks, Btw now is 03.05, will have a test at 10.00am, wish me luck
@WrathofMath
5 ай бұрын
Best of luck!
Great video, Can you please do a video on combined random variables I have a question if V~ Geom(p) with p = 0.67 and that W = 2V to Find P(W>=6) how do I approach such question! Mery Christmas btw
@nuche3931
2 жыл бұрын
That's a very interesting question,
@theroyaltyfamilyfanpage9542
2 жыл бұрын
@@nuche3931 I still cant figure out a way around it
@nuche3931
2 жыл бұрын
@@theroyaltyfamilyfanpage9542 would finding p(w>=3) work
Bro you saved me!
@WrathofMath
Жыл бұрын
Glad to help - thanks for watching!
Is the number theory video coming
liked immediately when i saw the christmas getup
@WrathofMath
10 ай бұрын
Haha thank you! I know it's distracting to some viewers but I get a real kick out of it.
Thanks. Your consciousness is eternal. You leave your body with your energetic bodies (mind is one of them), and you still exist after death.
If I don't talk nonsense, the 4 colors theorem say there are no 5-colorable graph, no ? (in the sens 4 colors could be used)
I understand it like If vertices number is odd is bipartite if it is even it is not bipartite sorry for bad English if any mistakes
@musabsarjo
5 ай бұрын
So i discovered that i am wrong 😂😂
But how can we prove that a given graph has no odd cycles ?
I think that is a little bit similar to "four color theorem"🤔
This guy is perfect in 1.25x
man looks like timothee chalamet if he was a cs student
THAKSKSKSKSKSKS