What are Planar Graphs? | Graph Theory

[@WrathofMath]

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! kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin Graph Theory course: kzbin.info/aero/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH Graph Theory exercises: kzbin.info/aero/PLztBpqftvzxXtYASoshtU3yEKqEmo1o1L

[@SYLXM]

I sit in class feeling like a failure for not being able to understand this stuff, and then you clear up the topic nearly every time. Your series on graph theory have been an absolute savior. You are so good at describing these concepts, I wouldn't be surprised if you used a teleprompter! Such elegant explanations.

[@WrathofMath]

Thank you so much!

[@lucassilva7194]

exams are in a week. This channel helped me a lot. Especially when my teacher made all of discrete math seem so complicated when it was just this simple and understandable. Thanks a lot man.

[@WrathofMath]

I'm so glad my lessons helped, thanks a lot for watching and best of luck on the exams!

[@PunmasterSTP]

Hey how'd your exams go?

[@lucassilva7194]

@@PunmasterSTP i passed. went better than i had hoped for lol.

[@PunmasterSTP]

@@lucassilva7194 I’m really glad to hear that!

[@jack-ci8je]

This video came out a few days after my discrete math final lol I needed this

[@WrathofMath]

Sorry it was late haha! But thanks for watching and it's good to be talking about planar graphs at last!

[@PunmasterSTP]

Oh man, sorry! How'd the class and the final go?

[@igorsun8619]

jeeeeeez, the two moments you came up with EulerIdentity and examples of non-planar are just amaaaaaaaaazing!!! How interesting they are woah!

[@WrathofMath]

Thanks for watching! I agree - they're really awesome and the proofs that follow this in my graph theory playlist are a bunch of fun as well! kzbin.info/aero/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH

[@rominamehrabi2647]

You just saved my assignment's life, Thank you!

[@WrathofMath]

Glad to help, thanks for watching!

[@Vanshika-rz3ok]

Your teaching methods are good and I am from India

[@WrathofMath]

Thank you!

[@sourabhahegde9690]

Thank you so much! I have an exam tomorrow and you are a life saver!

[@WrathofMath]

My pleasure! Thanks for watching and good luck on your exam! If you're looking for more graph theory, check out my playlist: kzbin.info/aero/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH

[@PunmasterSTP]

I know it's been a few years, but how did your exam go?

[@ChocolateMilkCultLeader]

You are a great great person. Thank you

[@HIRANYAKSHIKSHIRSAGAR]

your explanation is amazing!!!!!!. thankyou so much sir.

[@WrathofMath]

Most welcome!

[@chittytherobot]

wow ! why werent you my TA in school for the Graph Theory course ! loved your video this is absolutely awesome. BTW - How is it possible to draw K33 on a coffee cup , wouldnt I still end up crossing the final edge ? ( or am I doing something goofy like .. drawing over the handle of the cup ?)

[@WrathofMath]

Thanks a lot! So glad the lessons are helpful, and if you haven't already be sure to check out my Graph Theory playlist: kzbin.info/aero/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH As for drawing K33, as you can imagine that is difficult to answer in text. Check out this video, around 13:20 I think: kzbin.info/www/bejne/jKemqqeAq8lnfpI If you were not able to do it, it would be because you're NOT doing something goofy like drawing over the handle - drawing over the handle is the key since it allows you to effectively make one edge jump right over another - pretty slick!

[@PunmasterSTP]

It's plane to see: your channel's awesome! 👍

[@mike_the_tutor1166]

Do you have any interest in graceful graphs? If so, I suggest a video on the classes which have been proven graceful. I haven't dug into those proofs myself, but I assume they're difficult. However, many classes have been proven by construction, or in other words, an algorithm for labeling the vertices. That makes it easy to demonstrate the algorithm on examples, even if the formal proof is too difficult to explain. Just another thought. As always, take it or leave it. Keep enjoying the math and stay swanky!

[@WrathofMath]

I have studied up on graceful graphs a little bit, they might be fun to talk about after finishing this week’s marathon of planar graph videos! Once all is said and done, and I take the countless hours to sort my playlist, we will have a very excessive first course in graph theory playlist! What I recall from my last readings on graceful graphs, is thinking “boy, this stuff could be clunky to explain” haha, but I haven’t thought that much about presenting the material, so it might be no problem with some practice! Really appreciate the great ideas! They’re all in my notes, and they’ll be coming down the pipe! Thanks for the support, and may we all stay swanky in these difficult times!

[@mike_the_tutor1166]

@@WrathofMath lol

[@Peachess1111]

The best maths teacher exists 🙌

[@justsomeboyprobablydressed9579]

Great presentation!

[@WrathofMath]

Thank you kindly!

[@mzarinchang3744]

The vertices of same color should be adjacent or should not?

[@Ahadi237]

Hello sir, please explain weakly modular graphs and its properties !

[@Ahadi237]

Please explain Cage- amalgamation graph, how we cane find it? thanks

[@yarafares8918]

well explained :)

[@WrathofMath]

Thank you!

[@LearningCS-jp4cb]

That outro is 🔥, gives vibes of math researcher playing key role in ww3 winning lmaoo

[@WrathofMath]

Hahaha thank you!

[@sagnik.math7]

very very informative

[@WrathofMath]

Glad to hear it! Thanks a lot for watching, and if you're looking for more graph theory, check out my graph theory playlist! kzbin.info/aero/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH Let me know if you ever have any requests!

[@giorgiovasta7128]

Thank you very much

[@WrathofMath]

Glad to help - thanks for watching!

[@Ahmed-Radio]

Interesting thing about thus topic is that any nonplaner graph , Must containe any of K3,3 or K5 or both....

[@WrathofMath]

Indeed, it's a very surprising result!

[@cybervigilante]

I was looking at a couple of graph theory primers, and they both started with geographic areas. They mentioned the edges couldn't cross. What I want to know is Why the edges can't cross. What am I missing?

[@WrathofMath]

Thanks for watching and that is perhaps a result of the context in which graphs were introduced in those primers. I couldn't tell you for sure without seeing them though. When we represent maps of geographic areas with graphs, we typically represent regions of the map by vertices, and join vertices if their corresponding regions share a border. Drawing a graph from a map in this manner will result in a graph with no edge crossings (so long as you draw it with some care), and a major area of study in graph theory is that of planar graphs, which are graphs that can be drawn in the plane with no edge crossings. Outside of this context (and perhaps some others I am forgetting/am unaware of), edge crossings are not especially important. We can draw a graph with or without edge crossings, it doesn't change what the graph is - a set of vertices and a set of edges consisting of two-element subsets of the vertex set. See my lesson "What is a Graph?" for that definition if you're not familiar with it. And if you haven't already, check out my graph theory playlist! kzbin.info/aero/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH

[@geethasankar2338]

Superb

[@WrathofMath]

Thank you, I am glad it was helpful! If you haven't already, check out my graph theory playlist for more! kzbin.info/aero/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH

[@atiehgebrine4255]

can we use euler formula to prove a graph is plannar?

[@calantockarenviloria3966]

Thank you

[@WrathofMath]

My pleasure, thanks for watching!

[@uymichaeljacksonb.5128]

Thamkyou

[@WrathofMath]

My pleasure! Thanks for watching and check out my graph theory playlist for more! kzbin.info/aero/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH

[@savithria1167]

Super

[@WrathofMath]

Thank you!

[@gabrielpereiramendes3463]

#Excelent!

[@ZeroTwo00002]

U R SO (good)^2 !

[@WrathofMath]

Thank you!

[@thunderstorm178]

Idea: Take a simple proof and complexify it so much

[@salonisharma9479]

Uff so relatable 😂

[@FishSticker]

You look like a slightly nerdier Will wood

[@WrathofMath]

Grateful for the slightly

[@asterynn941]

you look like logic

[@WrathofMath]

Haha, maybe a little! Thanks for watching, and if you like rap, check out my math rap channel! kzbin.info/door/Q2UBhg5nwWCL2aPC7_IpDQ

[@KrejgMuys]

Great 👍