[Discrete Mathematics] Planar Graphs

We look at planar graphs and how to determine if a graph is planar or not.

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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.

[yeriichi]

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

[kiana]

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?

[Wagari]

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

[Colonies_Dev]

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

[riteshchaudhary]

"I cant do it thats why its not planar" and "kuratowski is a very very sexy mathematician" LOL

Very well explained, thanks!

[revowolf]

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

[Elilife]

Thanks, man! This video helped me a lot!

[kenilpatel]

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

[pax]

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

[khadijahflowers]

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?

[WanderlustBites]

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

[mohamadhasan]

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

[NoName-qivx]

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?

[catarina]

Your video is very helpful! Thank you very much!

[nhorcute]

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

[palakjainchannel]

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

[adityarjl]

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

[badnam]

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?

[Kamnuma]

You are so good to explain. Thank you!

[shubhamjhiknaria]

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