[Discrete Mathematics] Graph Coloring and Chromatic Polynomials

We talk about graph coloring and hwo to construct chromatic polynomials.
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We introduce graph coloring and look at chromatic polynomials.
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.

[@Blum962]

Best explanation I've seen! Thank YOU!

[@prashannakumar570]

"gonna put black cuz you can see that so well" lololol

[@aliawied2713]

Thats's rude and racist . . . . jk sry

[@wardotard]

Only because the black shows so well, two thumbs up! Oh, one thumb up. Truthfully, thanks for your videos and everything you have done for me the past year, you rock!!!!

[@NeelSandellISAWESOME]

At 1:17, shouldn't {a, b} be in the edge set, not the vertex set?

[@avhnfq]

I have an exam today, appreciate it!

[@nattaphumjampalee206]

Im here cuz tomorrow i have an exam . Im so sick with education and thank you

[@HamsaShehadeh]

how about the point that dont connect to any other point? what should i color it? a different color that no point got it? or same as any point color?

[@ashishnegi3848]

Best explanation about COLORING.

[@coxixx]

Hi i have learned so much things from you. thank you so much.from Iran

[@thelastcipher9135]

when counting the chromatic number of a cycle like the one you did near the end of the video, would it make sense if we divide by the number of vertices since we can rotate the cycle n times, where n is the number of vertices, to avoid overcounting...?

[@deepakvkashyap]

really helpful! thanks a ton! :)

[@paulaje9918]

thank you very much for this perfect explanation

[@arijitbagchi2197]

very nicely explained!!thanx a ton!

[@sweetygupta7552]

well explained sir straight to the concept thanku :)

[@vivekn993]

XD

[@zolo8887]

Thank you man! from Syria and Sweden. I am a big fan of yous.

[@chimesilas]

Hello Trev, you mentioned everything except how to find the chromatic polynomial of an incomplete graph. eg. when 2 edges are missing from a k5 and you are required to find the chromatic polynomial of that graph, please tell me what to do or anyone can please respond. Thanks

[@chimesilas]

Thank you very much. Am very grateful. God Bless you

[@iamlazyboy98]

Have a quizz tomorrow about this and I'm not able to access the course materials you saved me

[@justanaverageguy4739]

Thank you u saved me

[@timelygoose]

Thank you sir

[@heilyx]

Thank you! It helped me a lot :)

[@user-hi4lc7co6x]

to the point

[@sperera5916]

Trev, please explain this. For the path, it is L, L-1, L-1, L-1... but for the K graph, it is L, L-1, L-2, L-3. Why the difference, if we also say L-1, L-1.. this should be fine as L Lambda means number of colors.

[@sperera5916]

I think I started to understand it, K graph, we can't use a color on and off. We can use a color on and off only for paths. For K Graph, if a color is used, that can't be used again ever. I hope I am right.

[@arnabsaha8066]

the videos are very helpfull..!!!

[@federicoagostinelli9149]

When you use K, you mean a "complete" graph, am I right?

[@futureacid1997]

thank you for this video.. it just helped me a lot :P

[@nvsabhishek7356]

Thank you.

[@improbir]

quality study material

[@khmielnitzkythomas8846]

Thank you!

[@amitrajitbose6854]

Very nice demonstration

[@SwapnilSarkar]

Amitrajit Bose Target found!😂

[@amitrajitbose6854]

Swapnil Sarkar Haaahhhahhaa😂😂😂 Haa bhai. Internal er jonno 😷😪

[@SwapnilSarkar]

Amitrajit Bose Same here xD xD

[@sourav5562]

Great video :)

[@natarajanb1714]

x(k m,1) problems chromatic number 2 is ok but coloring fist vertex1 pink color common vertex green vertex 2 again green. is it correct sir, bcz both common vertex and vertex2 posses same color and connected (adjacent one). plz reply

[@sperera5916]

Hello Trev, at 5:48, the sequence is simplified as L!/(L-n)!. What did you derive that simplification? Can you direct me to an online article please. Thank you

[@sperera5916]

Permutation factorials?

[@Trevtutor]

Yes. Exactly the same.

[@spicy_wizard]

i am interested to know more of graph coloring problem. In Tsinghua University Discrete Math, they dive into this topic way deeper than the fancy intro you have done.

[@karishmazsweblog5561]

thankuh so mch :) i understood so well ;)

[@abhinavs03]

yo da real MVP mate :)

[@siddhantsingh4870]

Thanks 👍

[@visakh_vijayakumar_]

Thanx.. Great video. :-)

[@S_O_EVERYTHING]

This uses greedy algorithm and it doesn't always give the right answer. The way you process the vertices also matter. I just had an end semester exam and the answer was 3 but you can get 4 as an answer as well if you process the vertices in a different way. Start with different vertices , different time.

[@rohiljain2838]

c should be lamdaa - 2 cant be same as d. Is that right??

[@FaraazThePhenom]

I was also confused but after thinking for a while, lambda is actually not a color its the number of colors used so when we reach c we are not using a new color that is the reason why the value doesnt change

[@rohiljain2838]

thanks a ton brother

[@FaraazThePhenom]

Anytime man

[@DiptakBanerjee]

you did not show the actual procedure to obtain a chromatic polynomial for ANY graph. DUH..

[@santi5655]

thanks, what program do you use?

[@Trevtutor]

Windows Journal

[@santi5655]

Thanks:)

[@debusinha9015]

If handwritings were people this ones a hipster