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! ruclips.net/channel/UCyEKvaxi8mt9FMc62MHcliwjoin Graph Theory course: ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH Graph Theory exercises: ruclips.net/p/PLztBpqftvzxXtYASoshtU3yEKqEmo1o1L
I need this teacher in my engineering college best teacher I have ever seen 🙏😭❤️❤️❤️❤️❤️❤️❤️. His teachings skills are god level. ❤️❤️❤️❤️ Love from India ❤️🙌.
So glad to hear it! Thanks for watching! Be sure to check out my Graph Theory playlist if you're looking for more graph theory lessons, many more to come! ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
Thanks for watching, I am glad it helped! Sorry it took so long to start getting to this, it has been a gnarly couple of weeks for me, but production will be ramping up!
This I got while searching for clique complexes,although it's little bit different but it helps me to understand what a clique is.. Thank you so much. Can you please make a video for clique complexes as well?
Thanks for watching, and for the question! I am not familiar with clique complexes so don't expect a lesson soon, but I will study them and may do a lesson on them in the future, thanks for the request!
I'm glad to help! Thanks for watching, and check out my Graph Theory playlist if you're looking for more: ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
If I want to count how many cliques are in a graph, do I count subcliques as well? For example the graph in your example had cliques {a, b, c, f} with subcliques such as: {a, b, c}, {a, b, f}, {a, c, f}, {b, c, f}. Does the graph than contain 1 clique (because all the other cliques are sub cliques) or does it contain 5 and we just count all of them, no matter if they are sub-cliques or not?
Thanks for watching and good question! If you're asked to count the cliques, I'd say it's a pretty ambiguous question. If I was asked to simply "count the cliques" I'd count all cliques, since the question doesn't specify, and so we'd have 5 nonempty cliques. But it'd make more sense to count maximal cliques, only those that aren't subsets of larger cliques.
Glad to hear it, thanks for watching! If you're looking for more graph theory, check out my graph theory playlist! ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
It's a great software, Notability on an iPad Pro. I only use it for lessons, I have other apps I prefer for taking notes, but Notability is a really good option for notes too!
Good idea! Thanks for watching and for the request, I will try to fulfill it as soon as I can! Unfortunately I am sick at the moment, and cannot record lessons. But I expect to be better by next week, and will be right back to uploading new lessons every other day!
Here is the lesson on independent sets in graph theory! ruclips.net/video/0stavxEccvE/видео.html Thanks for the request, and let me know of any more specifics on the topic you'd like videos on, I do already have some more lessons planned on this topic!
@@vijayalekshmi4604 Please post video requests as their own comments rather than replies to other comments, just because RUclips usually doesn't notify me when people reply to comments so I often miss them! Thanks for watching and for your request, I'd love to fulfill it but I am not well read in Ramsey Theory, so I'd be hesitant to do a lesson on it. I can't say I'll have time to dig into it anytime soon, as I am currently studying financial mathematics primarily, but I regularly study different areas, and will definitely keep your request in mind going forward. I look forward to learning more about Ramsey Theory as well!
Hello sir, Thanks for your explanation. It’s very helpful. I need a video on Covering and Matching of Independent sets in graph theory. Can you please do it??
Confused. When you say set of vertices, does a clique need to have a minimum number of pairs of vertices? Or any two adgacent vertices make a clique, since they are a subset of vertices, they are adjacent and they are not the same vertice.
A clique does not need to have a minimum number of vertices. So indeed, any two adjacent vertices make up a clique, because their induced subgraph is complete. Additionally, every single vertex also is a clique, because its induced subgraph is K1, another complete graph. Thanks for watching and I hope that clears it up!
Thanks for watching and you mean do I get anything for making them? I really enjoy making the math lessons, it is fun to do and gives me a way to preserve my math knowledge - sometimes I use my lessons to re-learn things I forget! Thankfully, now that Wrath of Math has grown enough I get some money every month from ads, and also from my beloved supporters on Patreon! Here is a link if you're interested in checking that out: www.patreon.com/join/wrathofmathlessons
So a clique is a subset within the graph , and that subset must be a complete graph (K) or in other words , small complete graphs inside the main graph right?..
Thanks for watching and that's right! And remember we'll often find it convenient to consider the vertices in the complete subgraph as the clique as well. So the clique may the complete subgraph or the vertices within it.
Thanks for watching and just consider the definition of clique. Suppose we have a set C = { a, b } of 2 adjacent vertices. Does C satisfy the definition that each pair of distinct vertices from C is joined by an edge?
Thanks for watching and yes, those are cliques, I believe I mention {b, c, f} is a clique. However, under some definitions they may not be. Some definitions require cliques to be maximal, some don't, so you simply need to be aware what definition is being used - or what definition best suits your purpose. If you're writing a paper only concerned with maximal cliques, for example, it would make sense to make maximality part of the definition for convenience.
Hello and thanks for watching! I will do a video on decomposition of graphs as soon as I can! Got a few other requests to knock out first and I'll try to make a good lesson on it for you! Do you mean ideas for what field of math specifically to get a Ph.D in? Or do you mean ideas for a dissertation during your Ph.D? Either way I don't think I'm the best person to ask because I have not pursued a Ph.D, so I wouldn't be able to give you any advice or suggestions from first hand experience. If you are in the middle of getting a bachelor's degree, or have one, or plan on pursuing one, I'd ask your math professors more about this, as most of them probably went through a similar path to what you're considering. Good luck!
Thanks for watching and the request! I have wanted to do this topic for a while, it's very fascinating. Not sure when I'll get to it though. I want to make sure my explanations do it justice!
You're very welcome - thanks for watching! If you're looking for more graph theory, check out my playlist! ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
@@WrathofMath Thank you sir. I've been searching for it since yesterday, but I can't find anything from Google or RUclips, I didn't find anything that was easy to understand.
@@WrathofMath I’m searching all over the internet but I didn’t see any convincing details on Ramsey numbers yet!! And I really need to understand 🙄🥺 how do we find the exact solution R(3,3)=6, R(4,4)=18 and even big numbers!! How can I get to know the exact value!! 😶
By "exact solution" do you mean how to prove the equalities you listed? As for bigger numbers, we don't know the other Ramsey numbers like R(5,5), R(6,6) and so on.
Thanks for watching and I will answer with a question. A clique is a set of vertices that are all adjacent to each other. So, if we consider a subset of a clique, must those vertices in the subset all be adjacent to each other?
Shouldn't cliques be MAXIMAL COMPLETE subgraphs ? I would claim that C2 is not a clique since it is complete but not maximal complete. C1 is the maximal complete version of C2.
Yup, it all depends on the definition being used. Requiring cliques to be maximal seems fairly common, and not requiring them to be maximal is common too. Thanks for watching!
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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!
ruclips.net/channel/UCyEKvaxi8mt9FMc62MHcliwjoin
Graph Theory course: ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
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Thank you for making this! Its much easier to understand once its visualized like this
So glad it helped! Let me know if you ever have any questions and thanks for watching!
I will report about this in my masteral class. You just saved my life ❤
So glad it helped, thanks a lot for watching!
the guitar part was nice thank you for making me exam night alittle better
❤❤❤❤
Thank you! Good luck on the exam/I hope it went well!
Super clear, easy to understand. Cheers!
Thank you, I'm glad to hear it!
absolutely perfect, keep going !!
Thank you! I'm making as many lessons as I possibly can! Let me know if you have any requests!
excellent explanation, i really appreciate you breaking down each piece of logic as the notation can get confusing at times :)
Glad it was helpful!
I need this teacher in my engineering college best teacher I have ever seen 🙏😭❤️❤️❤️❤️❤️❤️❤️. His teachings skills are god level. ❤️❤️❤️❤️ Love from India ❤️🙌.
Thanks so much! Glad it helped!
Good stuff bro, much better explanation here than the sliders the teacher gave us.
Thank you for watching and for your kind words! I am glad it helped. Let me know if you ever have any video requests!
Clear and precise. Thanks from 🇮🇳
I'm glad you found it clear and thanks for watching! It's great to be able to reach people all over the world, and many from India!
Wow, your videos really help things to...sink in! 👍
Thank you
Your way of explaining is mind blowing
Thanks and welcome!
Very easy to understand it....
Thanks.... from Pakistan..
Thanks a lot. Quick and straight forward explanation. Got it right away.
Glad to hear! You're welcome and thanks for watching!
Amazing , i loved it. Thanks a lot sir
My pleasure, thanks for watching!
thank you so much for this! this saved me a lot of time
So glad to hear it! Thanks for watching! Be sure to check out my Graph Theory playlist if you're looking for more graph theory lessons, many more to come! ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
Pleasant, perfect exposition.
Thank you!
Thank you so much sir for your clearly clarification!
This is so good! Could you explain how to reduce CNFSAT to clique and vise versa? Thank you so much.
good, clear explanation.
You're a good lessoning teaching guy. Lol, great explanation !
Thank you! Let me know if you ever have any video requests and I'll do my best to make another good lesson on it!
Best video on clique. Thanks
Thanks for the gift Sean
Thanks for your explanation. It’s very helpful. Looking forward to the following videos about this topic.
Thanks for watching, I am glad it helped! Sorry it took so long to start getting to this, it has been a gnarly couple of weeks for me, but production will be ramping up!
Haha a custom guitar played outro is pretty cool!
You da Graph Theory master in RUclips
This I got while searching for clique complexes,although it's little bit different but it helps me to understand what a clique is.. Thank you so much.
Can you please make a video for clique complexes as well?
Thanks for watching, and for the question! I am not familiar with clique complexes so don't expect a lesson soon, but I will study them and may do a lesson on them in the future, thanks for the request!
@@WrathofMath also if possible a video on comparability graph too.
loved this class
This is very easy to comprehend. Thanks a lot!
You're welcome, I am glad it helped! Check out my Graph Theory playlist if you're looking for more: ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
Thank you for making this clear
Please explain the difference between clique and pathwidth
Please do a video of inverse domination graph
You are my graph guru🙏
Very good explanatory video
Thanks a lot Sir 👍 for awesome Explanation 👌
My pleasure, thanks for watching! Check out my Graph Theory playlist for more! ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
Have you worked on spectral graph theory also?
Fantastic Video, keep up the great content. You're helping myself as a college student understand the material! I'm new to the subject
Thanks a lot! Good luck in college, and let me know if you ever have any video requests! I'm happy to help when needed!
Wrath of Math Ayeee thank you so much!! And I will do!! Thx!
explained everything well & thorough !
Thank you, I am glad it was clear and thanks for watching!
Thanks for the clear explanations!
You're very welcome! Thanks for watching!
Your video helped me a lot, thanks !
Glad to hear it! Thanks for watching, Pablo!
The best explanation out there 💕
Thank you, that's what I strive for!
Fantastic explanation sir
I am glad it was clear, thanks for watching!
Wow! Well-explained ❤ thanks so much
nice explanation 👍
Thank u so much 4 ur explanation 😍it helps me lot
So glad it helped, you're welcome and thanks for watching!
I like the idea of song at the end,
What is the Largest Clique of an undirected graph? Please explains in details............................
please explain what clique separable graphs are
Man what a heck are you talking about? You turned something so simple into quantum physics.
Sorry it wasn't clear, do you have any questions I can help clear up?
@@WrathofMath
Yes in story writing how do I create a good clique?
Great video, super helpful!
Very Clear. thanks.
Glad to hear it, thanks for watching and check out my graph theory playlist for more! ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
Omg this was so clear thanks much
My pleasure, thanks for watching and let me know if you ever have any questions!
Im really thankful to u 🙏🤜
I'm glad to help! Thanks for watching, and check out my Graph Theory playlist if you're looking for more: ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
If I want to count how many cliques are in a graph, do I count subcliques as well? For example the graph in your example had cliques {a, b, c, f} with subcliques such as: {a, b, c}, {a, b, f}, {a, c, f}, {b, c, f}. Does the graph than contain 1 clique (because all the other cliques are sub cliques) or does it contain 5 and we just count all of them, no matter if they are sub-cliques or not?
Thanks for watching and good question! If you're asked to count the cliques, I'd say it's a pretty ambiguous question. If I was asked to simply "count the cliques" I'd count all cliques, since the question doesn't specify, and so we'd have 5 nonempty cliques. But it'd make more sense to count maximal cliques, only those that aren't subsets of larger cliques.
Really amazing I got a clear picture about clique ❤️
Glad to hear it, thanks for watching! If you're looking for more graph theory, check out my graph theory playlist! ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
Amazing video, can you explain n-clan and n-club?
Thanks for watching and for the request! It's a little late, but here it is! ruclips.net/video/LqPHg9uNp-o/видео.html
very helpful, thanks!
You're welcome - thanks for watching! If you're looking for more graph theory, check out my playlist! ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
Good job, way to go. Thanks.
You're welcome, and thanks for watching!
Can i know the name of the software you are using as a board? Its really good
It's a great software, Notability on an iPad Pro. I only use it for lessons, I have other apps I prefer for taking notes, but Notability is a really good option for notes too!
please do a video on independent set of a graph
Good idea! Thanks for watching and for the request, I will try to fulfill it as soon as I can! Unfortunately I am sick at the moment, and cannot record lessons. But I expect to be better by next week, and will be right back to uploading new lessons every other day!
Here is the lesson on independent sets in graph theory! ruclips.net/video/0stavxEccvE/видео.html
Thanks for the request, and let me know of any more specifics on the topic you'd like videos on, I do already have some more lessons planned on this topic!
Can you do a video on the basics of Ramsey theory ?plzz
@@vijayalekshmi4604 Please post video requests as their own comments rather than replies to other comments, just because RUclips usually doesn't notify me when people reply to comments so I often miss them! Thanks for watching and for your request, I'd love to fulfill it but I am not well read in Ramsey Theory, so I'd be hesitant to do a lesson on it. I can't say I'll have time to dig into it anytime soon, as I am currently studying financial mathematics primarily, but I regularly study different areas, and will definitely keep your request in mind going forward. I look forward to learning more about Ramsey Theory as well!
Can you please tell me how to find strong metric dimension?
Hello sir,
Thanks for your explanation. It’s very helpful.
I need a video on Covering and Matching of Independent sets in graph theory. Can you please do it??
I'm glad it helped and thanks for watching! Is this what you're looking for? ruclips.net/video/chdr2aj4FUc/видео.html
@@WrathofMath thank you so much sir. This is exactly what I was looking for.
What is the least number of vertices in a clique?
Perfect. Can you tell me which software you are using for the board?
Thank you! These lessons are recorded on the app Notability on iPad Pro!
Excellent
so is a,c,f also a clique in this graph?
Does {b,d,e} FORM A CLIQUE?
is {b,c,d,e,f,a} is a clique in this graph?
Confused. When you say set of vertices, does a clique need to have a minimum number of pairs of vertices? Or any two adgacent vertices make a clique, since they are a subset of vertices, they are adjacent and they are not the same vertice.
A clique does not need to have a minimum number of vertices. So indeed, any two adjacent vertices make up a clique, because their induced subgraph is complete. Additionally, every single vertex also is a clique, because its induced subgraph is K1, another complete graph. Thanks for watching and I hope that clears it up!
Do you benefit from these great vids?
Thanks for watching and you mean do I get anything for making them? I really enjoy making the math lessons, it is fun to do and gives me a way to preserve my math knowledge - sometimes I use my lessons to re-learn things I forget! Thankfully, now that Wrath of Math has grown enough I get some money every month from ads, and also from my beloved supporters on Patreon! Here is a link if you're interested in checking that out: www.patreon.com/join/wrathofmathlessons
So a clique is a subset within the graph , and that subset must be a complete graph (K)
or in other words , small complete graphs inside the main graph
right?..
Thanks for watching and that's right! And remember we'll often find it convenient to consider the vertices in the complete subgraph as the clique as well. So the clique may the complete subgraph or the vertices within it.
Any other similar algorithm or efficient algorithm than clique partition algorithm...?
How about if we have 2 vertices? example, C={b, c}. Can we consider it a clique?
Thanks for watching and just consider the definition of clique. Suppose we have a set C = { a, b } of 2 adjacent vertices. Does C satisfy the definition that each pair of distinct vertices from C is joined by an edge?
@@WrathofMath Yes. Thank you. Can you also discuss Clique Graph. Thanks and More subscribers to come!
Thanks!
But can we say that {b, c, f}, {a,b,c}, {a,c,f}, are also clicks? of they must be taken as max adjacent set?
Thanks for watching and yes, those are cliques, I believe I mention {b, c, f} is a clique. However, under some definitions they may not be. Some definitions require cliques to be maximal, some don't, so you simply need to be aware what definition is being used - or what definition best suits your purpose. If you're writing a paper only concerned with maximal cliques, for example, it would make sense to make maximality part of the definition for convenience.
@@WrathofMath Thank you very much.
Hi could you do a video explaining K-cores in graph theory
Absolutely, thanks for watching and for the request and sorry for the late reply!
Sorry for the long wait, thanks for the request! :) Here is the lesson!
ruclips.net/video/rHVrgbc_3JA/видео.html
Thank you so much ❤❤❤❤❤
My pleasure - thanks for watching!
Hello sir ,
I need a video on decomposition of graph. Can you please do it??
And give me some ideas to do Ph.D in this field
Hello and thanks for watching! I will do a video on decomposition of graphs as soon as I can! Got a few other requests to knock out first and I'll try to make a good lesson on it for you! Do you mean ideas for what field of math specifically to get a Ph.D in? Or do you mean ideas for a dissertation during your Ph.D? Either way I don't think I'm the best person to ask because I have not pursued a Ph.D, so I wouldn't be able to give you any advice or suggestions from first hand experience. If you are in the middle of getting a bachelor's degree, or have one, or plan on pursuing one, I'd ask your math professors more about this, as most of them probably went through a similar path to what you're considering. Good luck!
Hi. Would you please make a video on chromatic polynomials! Thank you.😇
Thanks for watching and the request! I have wanted to do this topic for a while, it's very fascinating. Not sure when I'll get to it though. I want to make sure my explanations do it justice!
@@WrathofMath Thank you!😇
Superb! Thanks
Glad it helped and thanks for watching!
Thanks sir 🙏🏻
You're very welcome - thanks for watching! If you're looking for more graph theory, check out my playlist! ruclips.net/p/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH
Thank you :)
Thanks a lot!
Glad to help, thanks for watching!
Sir Do you have any video on Vertex transitive graph ?
Thanks for watching and I do not at the moment, but I will add it to my list and try to do it soon!
@@WrathofMath Thank you sir.
I've been searching for it since yesterday, but I can't find anything from Google or RUclips, I didn't find anything that was easy to understand.
Please explain Ramsey numbers
Thanks for watching, I will definitely get to Ramsey numbers sometime. Hopefully sometime this year, they're really cool!
@@WrathofMath I’m searching all over the internet but I didn’t see any convincing details on Ramsey numbers yet!! And I really need to understand 🙄🥺 how do we find the exact solution R(3,3)=6, R(4,4)=18 and even big numbers!! How can I get to know the exact value!! 😶
By "exact solution" do you mean how to prove the equalities you listed? As for bigger numbers, we don't know the other Ramsey numbers like R(5,5), R(6,6) and so on.
@@WrathofMath I mean how do we know that R(3,3)=6, R(5,5)= 45 etc etc? Is there any way to find out?
what is pathwidth?
Are all subsets of a clique also cliques themselves?
Thanks for watching and I will answer with a question. A clique is a set of vertices that are all adjacent to each other. So, if we consider a subset of a clique, must those vertices in the subset all be adjacent to each other?
@@WrathofMath Yes, they will have to be adjacent to each other so a subset should also be a clique I think.
Precisely!
I literally thought this was a video about social cliqusz
Shouldn't cliques be MAXIMAL COMPLETE subgraphs ? I would claim that C2 is not a clique since it is complete but not maximal complete. C1 is the maximal complete version of C2.
Oh you mentioned it in later :)
Yup, it all depends on the definition being used. Requiring cliques to be maximal seems fairly common, and not requiring them to be maximal is common too. Thanks for watching!
there are some definitions said that it should be a maximal complete subgraph
That’s correct!
@@WrathofMath thanks for your videos. I'm currently pursuing my graduates studies in math.
thank you
Thank you! 😊
Great Video!
Thank you! And thanks a lot for watching, I am glad it helped!
C2= {b,a,f} is also a clique
Thanks for watching and you're right!
TY , really usefull .!
Glad to hear it! You're welcome and thanks for watching!
Good job
Thank you for watching!
perfect!
I think I should explain in little deep about what is the concept actually.
thanks
No problem - thanks for watching!
What is Plex sir
Thanks for watching and for the request! Here is the k-plex lesson! ruclips.net/video/V2CgqTLWxvY/видео.html
You are the best
Thank you!