[Discrete Mathematics] Planar Graphs

Подписаться 272 тыс.

Просмотров 111 тыс.

50% 1

We look at planar graphs and how to determine if a graph is planar or not.
Visit our website: bit.ly/1zBPlvm
Subscribe on RU-vid: bit.ly/1vWiRxW
-Playlists-
Discrete Mathematics 1: • Discrete Math (Sets, L...
Discrete Mathematics 2: • Discrete Math (Countin...
-Recommended Textbooks-
Discrete and Combinatorial Mathematics (Grimaldi): amzn.to/2T0iC53
Discrete Mathematics (Johnsonbaugh): amzn.to/2Hh7H41
Discrete Mathematics and Its Applications (Rosen): amzn.to/3lUgrMI
Book of Proof (Hammack): amzn.to/35eEbVgLike us on Facebook: on. 1vWwDRc
Submit your questions on Reddit: bit.ly/1GwZZrP
In this video we introduce planar graphs, talk about regions, and do some examples.
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

Опубликовано:

28 июн 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 46

@yeriichi 4 года назад

6:20 LMAO was not expecting to hear sexy mathematician in a planar graph video

@CrittingOut 3 года назад

same lmfao

@kenilpatel7841 7 лет назад

That was amazing... Made my concept crystal clear... Thanx a lot :)

@WanderlustBites215 3 года назад

Amazing video..Really helped a lot. Thank you!!

@catarina2289 8 лет назад

Your video is very helpful! Thank you very much!

@JJ-xf2zy 7 лет назад

Helps me a lot, thanks!

@Eli4life 4 года назад

Thanks, man! This video helped me a lot!

@mikepointo5638 8 лет назад

Great explanation man!

@adityarjl6557 6 лет назад

u saved my life bro... great vid !!! :)

@kiana6672 7 лет назад

Hi Trev, for the last question when we try to find a homomorphism of K5, you added in the vertex 'e' by subdividing the edge (bf) into (be) and (ef). This eliminates the edge (bf) in the original graph where b and f were connected directly by the edge (bf) and also (be),(ef). Does it not matter that we just eliminate that edge?

@TheMinecraftMonopoly 3 года назад

I agree, It would mean that b has degree of 4 and f has degree of 5, but the original graph has b and f as 5, 6 respectively. I just added in an edge to my own copy as It is correct.

@FcBarcelonaKid 5 лет назад

Thanks for the help! God bless you

@revowolf7413 3 года назад

It would be really helpful if you put timestamps. Thanks!

@KansasFashion 6 лет назад

You are awesome!!!!!

@Wagari1000 8 лет назад

I can already see the A on my Discrete Math course, Thanks a lot man!!

@Kamnuma 6 лет назад

You are so good to explain. Thank you!

@pax1913 4 года назад

If I pass my Discrete test on Wednesday it'll be thanks to this

@PalakJainChannel 7 лет назад

what does crossing of edges mean? Do they cross only in 2d or can the graph be visualized in 3d as well?

@Trevtutor 7 лет назад

These graphs exist on a 2D plane.

@PalakJainChannel 7 лет назад

ok.. thanks! planar graphs are a bit confusing..

@Colonies_Dev 10 месяцев назад

love these videos, far more helpful than other channels, but the kuratowskis theorem section is marked kura taos keys in the timeline

@riteshchaudhary7784 2 года назад

"I cant do it thats why its not planar" and "kuratowski is a very very sexy mathematician" LOL Very well explained, thanks!

@mohamadhasan6560 3 года назад

Thanks for your nice lectures. May I know is an empty graph (a graph with no edges) a planner graph? How about graph G that is the union of an isolated vertex and a complete graph of order 2, is G planner? Thank you

@Bridgelessalex 3 года назад

(1) Yes, by definition, an empty graph is planar. (2) What do you mean by a complete graph of order 2? If you are referring to a complete graph with 2 vertices (which is essentially an edge), then yes, it is planar.

@khadijahflowers5566 6 лет назад

Since K5 is a complete graph and non planar and the notation for a complete graph is Kn, can we say that every complete graph where n > 4 is non planar?

@Trevtutor 6 лет назад

Yeah. Since every Kn graph where n > 5 has a K5 subgraph.

@nhorcute1478 3 года назад

is it possible to draw the edges of the graph in such a way that the edges do not cross?

@NoName-qi7vx 3 года назад

What about this criteria: For every planar Graph G = (V, E) wtih |V | = n, |E| = m ≥ 3: m ≤ 3n − 6 and For every planar Graph G= (V, E) with |V | = n, |E| = m ≥ 3 and without cycles of length 3: m ≤ 2n − 4 Does this work or are there problems?

@shubhamjhiknaria9562 4 года назад

Had a question...when we subdivide a graph can the degree of a vertex change?

@zakariamohamud6637 5 месяцев назад

When you subdivide a graph, the degree of a vertex may change. Subdividing a graph involves replacing an edge with a new vertex and two new edges. The new vertex is inserted along the original edge, splitting it into two separate edges.

@christopherrippel2958 7 лет назад

i was looking for a demoucron malgrange pertuiset algorithm video. writing it out and searching gave me nothing. any luck finding it on youtube?

@christopherrippel2958 7 лет назад

btw ur videos helped me out a lot in the past and for that i thank u

@promodkumarsinha 5 лет назад

Is forest a planar graph ?

@GG4EVA623 3 года назад

This is so hard to understand I tried to look up a level maths and this came up I'm so baffled now

@ruhanmuzaffar2012 7 лет назад

can i not siply use the formula m>=3n-6?(eulers formula)

@iliTheFallen 4 года назад

Hello Trev! The homomorphism concept u explained in the beginning does not seem correct to me when I compare it to the one explained here: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-RatkBWHUSqo.html . Are you sure that H is homomorphic to G?? Can't find a proper vertex maping function!!

@badnam3189 4 года назад

You prove non-planarity by showing that it has a subgraph that is a subdivision of k5 or k3,3, but how do you prove planarity then?

@emperor8716 6 месяцев назад

by drawing the graph in such a way that it is flat and no edges cross.

@merry6423 Год назад

我意识到了学英语的重要性

@spitfirelast8761 5 лет назад

9:41 I thought you said planar has no crossing edges? What sorcery is this?

@shlomi441 5 лет назад

"Planar" means "can be drawed as a plane graph". A plane graph has no crossing edges

@SanketAlekar Год назад

Hey Trev, it's homeomorphic, not homomorphic. Graph homomorphism is very different from homeomorphism.

@alperyuksel1726 3 года назад

I can't do it. therefore, it's not planar. □

@tldyesterday Год назад

6:18 Ayo?

@lamiasall4975 7 лет назад

Dude you can just use Euler's formula to count the vertices and edges ... It's more like proving you don't even need to draw

@wntrans1835 2 года назад

Euler's forumla is only good for checking if the current drawing of the graph is planar or not. It won't tell you if there is a different drawing of the graph that is planar which is the hard part.