Matchings, Perfect Matchings, Maximum Matchings, and More! | Independent Edge Sets, Graph Theory

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  • Опубліковано 25 сер 2024

КОМЕНТАРІ • 194

  • @WrathofMath
    @WrathofMath  3 роки тому +12

    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!
    ua-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin
    Graph Theory course: ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
    Graph Theory exercises: ua-cam.com/play/PLztBpqftvzxXtYASoshtU3yEKqEmo1o1L.html

  • @Anteater23
    @Anteater23 4 роки тому +118

    Did not expect to get an entire video to my question. Thank you!

    • @WrathofMath
      @WrathofMath  4 роки тому +17

      Thanks for watching! Wrath of Math is all about customer service, haha! It was just good timing - I was going to record and edit a lesson last night anyways; and I was perfectly happy to talk about matchings, so it worked out great! Glad to be able to help!

  • @TVSuchty
    @TVSuchty 4 роки тому +28

    Well done! Subscribed. You are on the best way of becoming a youtube legend for all computer scientists and mathematicians who are going to be tested in discrete mathematics!
    I like the color theory you use btw 🙂

    • @WrathofMath
      @WrathofMath  4 роки тому +4

      Thanks so much for your kind words and for subscribing! I'm glad to be able to help!

  • @aeturinagapavankalyanreddy3559
    @aeturinagapavankalyanreddy3559 4 роки тому +16

    very clean and clear explanation ever watched on this topic...Thank you

    • @WrathofMath
      @WrathofMath  4 роки тому +1

      Thanks for watching and for your kind words, glad you found the lesson clear!

  • @tortor2883
    @tortor2883 3 роки тому +22

    me to encouraging friend: Oh no, i got an F
    Encouraging Friend: 1:29

  • @robertcormia7970
    @robertcormia7970 2 місяці тому

    This was really helpful, I was lost trying to understand perfect matches in aromaticity (chemical graph theory) but this (and GPT-4) helped me make sense of it. The best part of the video, hands down, was the music at the end, we need more of that!

  • @saminyeaser3939
    @saminyeaser3939 3 роки тому +4

    Dear Wrath of Math.
    I would be very grateful if you make a video on flow networks and about the algorithms like...........Ford and fulkerson ...augmented paths.......max flow min-cut theorem...and topics related to this. And as always....best videos I have seen so far. Too good explanations and I just luv your videos :)

  • @elizabethwrightsman2027
    @elizabethwrightsman2027 3 роки тому +3

    You sir have a talent for explaining things in a manner that anyone can understand! You will get me through this semester of Graph Theory. Thank you!

    • @WrathofMath
      @WrathofMath  3 роки тому +2

      Thanks so much, Elizabeth! I hope you'll continue to find the lessons helpful and let me know if you ever have any questions! More (spooky) graph theory videos are on the way!

    • @PunmasterSTP
      @PunmasterSTP 2 місяці тому

      Out of curiosity, how'd your graph theory class go?

  • @nellyzepeda7990
    @nellyzepeda7990 4 місяці тому

    I have watched your videos this whole Winter semester to help me with my Graph Theory course. Thank you so much for posting these, they are extremely helpful and so well thought out, your explanations are amazing!

  • @Ian-bb7vv
    @Ian-bb7vv 2 місяці тому

    thx for the clear definition and explanation. You made an easy concept easy.

  • @FleurDeCersier
    @FleurDeCersier 3 роки тому +1

    Thank you. This is super helpful. Missed graph theory last semester because of illness and now I need it.

    • @WrathofMath
      @WrathofMath  3 роки тому +1

      You're welcome, I am so glad it helped! If you ever have any questions let me know, and I hope your illness is all gone!

  • @kirtipurohit1237
    @kirtipurohit1237 3 роки тому +2

    Thank you so much. It really helped me to clear my concepts. Please keep going! Thanks

    • @WrathofMath
      @WrathofMath  3 роки тому

      So glad it helped! Thanks for watching, and if you're looking for more graph theory be sure to check out my playlist: ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
      Let me know if you have any video requests!

  • @thefourthbrotherkaramazov245
    @thefourthbrotherkaramazov245 2 роки тому

    Bro, this channel is insanely good for getting into graph theory and combinatorics

    • @WrathofMath
      @WrathofMath  2 роки тому

      That's what I like to hear, thank you! Let me know if you have any requests!

  • @anmolbehl8572
    @anmolbehl8572 2 роки тому

    Very clean and understanding explaination for starters...

    • @WrathofMath
      @WrathofMath  2 роки тому

      Glad to help, thanks for watching! If you want more on matchings, check out my lessons on Hall's marriage theorem.
      ua-cam.com/channels/Q2UBhg5nwWCL2aPC7_IpDQ.html
      ua-cam.com/video/4tu-H4ES0fk/v-deo.html

  • @aerospace_andy
    @aerospace_andy 2 роки тому

    thank you very much! I understand it now. My slides were confusing.

  • @likithr.n9692
    @likithr.n9692 2 роки тому +1

    You were outstanding in terms of clarifying my understanding

    • @WrathofMath
      @WrathofMath  2 роки тому +1

      So glad to hear it, thanks for watching! If you're looking for more graph theory, check out my playlist! ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html

  • @yashaswani8813
    @yashaswani8813 Рік тому

    Beautifully explained with ample amount of examples to make concepts crystal clear. Love it!

  • @mizukashirei
    @mizukashirei Рік тому

    thank you very much tomorrow is my graph theory final exam and this vids is very helpful wish me luck

  • @milkosek
    @milkosek 3 роки тому

    Man, I read like 5 articles preparing for a colloquium and just your video helped to understand. I gave you a sub, keep up the great work and keep educating young engineers and mathematicians.

    • @WrathofMath
      @WrathofMath  3 роки тому +1

      So glad it helped! Thanks for watching and subscribing, and I will continue making the best lessons I can!

  • @tysontakayushi8394
    @tysontakayushi8394 3 місяці тому

    So well explained, amazing!

  • @ramster5678
    @ramster5678 4 роки тому +2

    Excellent video, great and clear explanation. Thank you for posting this.

    • @WrathofMath
      @WrathofMath  4 роки тому

      I'm glad it was clear, thanks a lot for watching!

  • @angelesfigueredo5740
    @angelesfigueredo5740 2 роки тому

    You have the gift of explanning. Thanks for you work

    • @WrathofMath
      @WrathofMath  2 роки тому

      So glad to help, thanks for watching!

  • @amaldas1048
    @amaldas1048 Рік тому

    Simple and clearer..Thank you

  • @kamranmehdiyev8561
    @kamranmehdiyev8561 3 роки тому +1

    Great ! I was looking for the topic "Maximum matching"

    • @WrathofMath
      @WrathofMath  3 роки тому

      Glad it helped, thanks for watching!

  • @ScientistRenzo
    @ScientistRenzo Рік тому

    As someone who’s dabbled in making videos, this is really high quality. Great and thanks

  • @NosBY44
    @NosBY44 Місяць тому

    Really good explanation! It would be good to also do some formal proofs of all this stuf, but still a really good way of getting an intuition

    • @WrathofMath
      @WrathofMath  Місяць тому

      Thank you! My playlist has a lot of proofs in it: ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
      A proof of Hall's Marriage theorem I believe follows this video in the playlist. Thanks for watching!

  • @minhanhpham2508
    @minhanhpham2508 2 роки тому +5

    Matchings: 00:00
    Maximal matchings: 06:28
    Maximum matchings: 08:35
    Perfect matchings: 10:55

  • @abhirama
    @abhirama Рік тому

    Excellent explanation. Was a very useful primer to solve assignment problems.

  • @muddassirghoorun4322
    @muddassirghoorun4322 4 роки тому +1

    That is the best explanation I have heard by far!

    • @WrathofMath
      @WrathofMath  4 роки тому +1

      So glad to hear it! Thanks for watching!

  • @ChenNanshan
    @ChenNanshan 3 роки тому

    Helps a ton! Thanks a lot! My 80-year old professor was even not able to explain them clearly.

    • @WrathofMath
      @WrathofMath  3 роки тому

      So glad it helped, thank you for watching!

  • @sanaaejaz1564
    @sanaaejaz1564 2 роки тому

    Nice explanation...and the last brushing up was also needed...thanks for the video

  • @mikeey
    @mikeey 3 роки тому

    Well done bro, understood in 15 min what the teacher could not explain in 2h, subscribed for sure :D keep up the great work and stay safe

    • @WrathofMath
      @WrathofMath  3 роки тому +1

      Thank you, so glad it helped! Thanks for subscribing and you stay safe as well!

  • @soumyadipmajumder902
    @soumyadipmajumder902 2 роки тому

    thank you sir for this lesson, it helps me a lot

    • @WrathofMath
      @WrathofMath  2 роки тому +1

      Glad to hear it, thanks for watching!

  • @ali_official3239
    @ali_official3239 4 роки тому +1

    Very clear explanation. Thank you

    • @WrathofMath
      @WrathofMath  4 роки тому

      You're welcome! Thanks for watching!

  • @user-dy2sn1ny5t
    @user-dy2sn1ny5t 2 роки тому

    Really nice video! This deserves more upvotes!

  • @SHASHANKRUSTAGII
    @SHASHANKRUSTAGII 3 роки тому

    That augmented path Algo, I learnt from Dr. A.R. Ranadey, IIT BOMBAY, INDIA. He explained it so well
    you are also good.

  • @PunmasterSTP
    @PunmasterSTP 2 місяці тому

    "Match"-ing is right, 'cause this playlist is fire 🔥

    • @WrathofMath
      @WrathofMath  2 місяці тому +1

      Appreciate you! 🔥🔥

    • @PunmasterSTP
      @PunmasterSTP 2 місяці тому

      @@WrathofMath And I appreciate you, what with your helping us to become academically independent, stay at the edge of our seats, and get set 👍

  • @felixlolll6220
    @felixlolll6220 3 роки тому

    This video save my discrete math. TY!

    • @felixlolll6220
      @felixlolll6220 3 роки тому

      Exam I mean.

    • @WrathofMath
      @WrathofMath  3 роки тому

      So glad it helped! Thanks for watching and let me know if you ever have any questions!

  • @abdulhameedafridi9524
    @abdulhameedafridi9524 11 місяців тому

    Perfect sir. I really appreciate your efforts, very helpfull

    • @WrathofMath
      @WrathofMath  11 місяців тому

      Thank you for watching!

  • @vartika_singh16
    @vartika_singh16 3 роки тому

    Please make a video on alternating path and augmenting path

  • @rayvinlai7268
    @rayvinlai7268 2 роки тому

    Thanks bro.that's really great explanation

  • @LearningCS-jp4cb
    @LearningCS-jp4cb Місяць тому

    @8:30 maximal definition is little confusing, because in lattice algebra, there is always a unique maximum element which is greatest compared to all other elements. But in graph theory, there can be many maximal matchings.

  • @hasnanadifah9974
    @hasnanadifah9974 4 роки тому +1

    thankyouu soo much this video is very helpful for me bcs tomorrow i've to do an exam but i still dont have any idea about the matching theory

    • @WrathofMath
      @WrathofMath  4 роки тому

      I am glad it was helpful and good luck on your exam! I'm not sure what you mean by "the matching theory". As far as matching theorems go, I have a couple of videos on Hall's theorem which you may be interested in.
      Introducing the theorem: ua-cam.com/video/Ihr6gMx7b9c/v-deo.html
      Proof: ua-cam.com/video/4tu-H4ES0fk/v-deo.html

  • @sanaaejaz1564
    @sanaaejaz1564 2 роки тому

    Pls make a video on augmenting paths as well

  • @erfankouloubandi8622
    @erfankouloubandi8622 3 роки тому

    The ending was epic

    • @WrathofMath
      @WrathofMath  3 роки тому

      Thank you! Here is a link to that full song: ua-cam.com/video/OKBdXOrpA2w/v-deo.html

  • @salimasalman7655
    @salimasalman7655 2 роки тому

    I loved the way u sum it all

    • @WrathofMath
      @WrathofMath  2 роки тому +1

      Thank you - I do my best! Matchings is a fun topic!

  • @unknownsender1275
    @unknownsender1275 4 роки тому +1

    Wow, how an excellent explanation! Thank u so much. Have a nice day!

    • @WrathofMath
      @WrathofMath  4 роки тому

      You're very welcome, I am so glad it helped and thanks for watching! A good day to you as well!

  • @RickRabelo66
    @RickRabelo66 Рік тому

    thank you! very helpful.

  • @thaliaft
    @thaliaft 2 роки тому

    great explanation!

    • @WrathofMath
      @WrathofMath  2 роки тому +1

      I do my best! Thanks for watching and check out my graph theory playlist for more: ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html

  • @rajivkumarkale
    @rajivkumarkale 3 роки тому

    Great explaination

  • @monoman4083
    @monoman4083 2 роки тому

    good, clear explanation. keep them coming please.

  • @vivekgodhasara8699
    @vivekgodhasara8699 3 роки тому

    amazing sir , so good explanation ,thanks a lot sir

    • @WrathofMath
      @WrathofMath  3 роки тому

      So glad it helped, thanks for watching! If you're looking for more on graph theory, check out my graph theory playlist! ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
      Let me know if you ever have any video requests!

  • @souravdey1227
    @souravdey1227 10 місяців тому

    Can you please do a detailed video on path partitioning of directed graphs?

  • @yashsahu2488
    @yashsahu2488 2 роки тому

    you are doing a great job brother..love the way u explain it.

  • @alexandrebailly9363
    @alexandrebailly9363 3 місяці тому

    It helps me to see a matching as a marriage. A matching edge is a marriage between 2 adjacent vertices. A vertex can belong to only one marriage. As many vertices as possible should get married. If the order of the graph is odd (odd vertex count) then at least 1 vertex will remain single.

  • @chinosts
    @chinosts Рік тому

    great video well explained.

  • @TUMENG-TSUNGF
    @TUMENG-TSUNGF 2 роки тому

    12:00
    Don't worry. I sometimes watch your video when I'm dropping my browns.

  • @markusperry7382
    @markusperry7382 3 роки тому

    "Thats a really good f" love it =)

    • @WrathofMath
      @WrathofMath  3 роки тому +2

      Haha, thank you! Every time I rewatch this video I am impressed by that f!

  • @crush_gamer6853
    @crush_gamer6853 2 роки тому

    hi i have this question to find maximal in a ring graph:
    Let p0, . . . , pn−1 be n processors on a directed ring that Dijkstra considered in his selfstabilizing token circulation algorithm (in which processors are semi-uniform, i.e., there
    is one distinguished processor, p0, that runs a different program than all other processors
    but processors have no unique identifiers). Recall that in Dijkstra’s directed ring, each
    processor pi can only read from pi−1 mod n’s shared variables and each processor can
    use shared variables of constant size. Design a deterministic self-stabilizing matching
    algorithm that always provides an optimal solution

  • @nina42703
    @nina42703 Рік тому

    Could you possible explain clearly max weight branching and how to condense a weigthed digraph? Thank you for your clear explaining I appreciate so much.

  • @hellboy8868
    @hellboy8868 3 роки тому

    Amazing explanation , thank you sir !

    • @WrathofMath
      @WrathofMath  3 роки тому

      No problem, thank you for watching! Check out my Graph Theory playlist if you're looking for more lessons on the topic, many more coming soon! ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html

  • @GeigerPancake16
    @GeigerPancake16 3 роки тому

    Very nice explanation, thank you!

  • @namdang540
    @namdang540 3 роки тому

    Holy crap this video is really good. Well-explained dude!

  • @guriea9394
    @guriea9394 3 роки тому

    Thank you for this video😊

    • @WrathofMath
      @WrathofMath  3 роки тому +1

      No problem, thanks for watching! If you're looking for more graph theory, be sure to check out my Graph Theory playlist! ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html

  • @niazazeez
    @niazazeez Місяць тому

    Can you post a video on the proof for Tutte's Theorem?

  • @nedimcanulusoy
    @nedimcanulusoy 3 роки тому

    It was an incredible and very helpful video, thanks a lot for your effort!

    • @WrathofMath
      @WrathofMath  3 роки тому

      Thanks so much for watching and I am glad it helped! Let me know if you ever have any questions!

  • @rianfaradillaratnaningutam2295
    @rianfaradillaratnaningutam2295 11 місяців тому

    What a great video, I'm learning graph theory for my undergraduate thesis, but I have some problem with paired domination number and upper bound on paired domination number(the gamma of upper bound and gamma the minimum cardinality). I could not get the exact example cause lack of journal that explain and give the example of them. Would you mind if you make a explanation video about these problem? thankyou

  • @mrx99_
    @mrx99_ 7 місяців тому

    i really forgot whatever i learned . Thanks

  • @vidorg5574
    @vidorg5574 7 місяців тому

    Thank you very much!

  • @jeanstaquet8953
    @jeanstaquet8953 3 роки тому

    Very good content !

  • @zuggrr
    @zuggrr 2 роки тому

    This is amazing, thank you so much !

    • @WrathofMath
      @WrathofMath  2 роки тому

      My pleasure, thanks for watching! If you're looking for more graph theory, check out my playlist! ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html

  • @TUMENG-TSUNGF
    @TUMENG-TSUNGF 2 роки тому

    "That's a really good f"
    Same, man, same.

  • @flo450
    @flo450 3 роки тому

    loved the explanation, thank you :D

    • @WrathofMath
      @WrathofMath  3 роки тому +1

      You're very welcome, thanks for watching!

  • @abdulhameedafridi9524
    @abdulhameedafridi9524 Рік тому

    Perfect sir.

  • @devathinnikhil6221
    @devathinnikhil6221 3 роки тому

    please do a video max matching min vertex cover theorem

  • @sina_mousavi79
    @sina_mousavi79 3 роки тому

    Thank u sooo much man! Very clear explanation👌

    • @WrathofMath
      @WrathofMath  3 роки тому

      My pleasure, so glad it was clear and thanks for watching!

  • @sinagarebaghi2281
    @sinagarebaghi2281 3 роки тому

    It was clear. Thank you!

    • @WrathofMath
      @WrathofMath  3 роки тому

      Glad to hear it! You're welcome and thanks for watching!

  • @normancontreras1696
    @normancontreras1696 3 роки тому

    Thank you for the clear explanation of matchings. It did help to see an example that is not a bipartite graph.

  • @mpymani8022
    @mpymani8022 2 роки тому

    Can you teach vizing's theorem please?

  • @rasoulghadimi3546
    @rasoulghadimi3546 3 роки тому

    Excellent

  • @thanmyintaung1454
    @thanmyintaung1454 Рік тому

    Could you explane "Rainbow numbers for matching"?

  • @shahjaysheeldipalbhai207
    @shahjaysheeldipalbhai207 2 роки тому

    excellent

  • @vgil80
    @vgil80 2 роки тому

    Can you explain what “matching polynomials”?

  • @sleaktrade
    @sleaktrade 2 роки тому

    Hi, could you make a video about minimum-cost perfect matching and different approaches to finding it?

  • @williamashbee
    @williamashbee 2 роки тому

    integer linear programming for matching would be useful.

  • @harishodzic6615
    @harishodzic6615 3 роки тому

    Hi man! Great explanation and a great video! My question is: what videos from your graph theory playlist are essential and must-see(and know) for understanding the matching concept and being able to write a paper on it? I am a newcomer to graph theory and I have this as an assignment, and I think that your channel is a massive help for it. Thanks in advance!

  • @lancepit8161
    @lancepit8161 4 роки тому +1

    Thanks! Subscribed.

    • @WrathofMath
      @WrathofMath  4 роки тому

      Thanks for watching and subscribing!

  • @Jakob_Thom
    @Jakob_Thom Місяць тому

    You are awesome!

  • @aishwaryasam5805
    @aishwaryasam5805 2 роки тому

    amazing

  • @nlingamani
    @nlingamani 4 роки тому

    Can you give an idea about Augmenting and alternating path

  • @peifumo7416
    @peifumo7416 2 роки тому

    Wow you're a mathematician, rapper, and guitar player! How long have you been playing guitar? What's your music background?

    • @WrathofMath
      @WrathofMath  2 роки тому

      Yes, there is a lot to enjoy in the world! I began with saxophone when I was in 6th grade or so, and then piano, and a bunch of other stuff, I only started learning guitar in college. Mostly self taught in everything aside from saxophone and some piano lessons. Started rapping 2013 or 14. Do you play music?

    • @peifumo7416
      @peifumo7416 2 роки тому

      @@WrathofMath Yes there really is a lot to enjoy :) That's a lot of instruments! I've also been trying to learn the piano and started during covid times.

  • @amanuelnigatu4621
    @amanuelnigatu4621 8 місяців тому

    tnx man

  • @aayush6273
    @aayush6273 3 роки тому

    Please Explain Minimal Matching too.

    • @WrathofMath
      @WrathofMath  3 роки тому +1

      Thanks for watching and I am not sure what you mean. We can make a matching as small as we want, since it is just a set of edges that are not adjacent to each other. We could take any one edge from a graph to be a "minimal" matching, since there would be no matching that is a proper subset of it.

  • @hatenrashid4057
    @hatenrashid4057 4 роки тому

    thank you for your effort, and I have question; the alpha prime (G)=3?🐝💐

  • @saumyaranjannayak2101
    @saumyaranjannayak2101 4 роки тому +1

    best on youtube

  • @peimanmohseni9239
    @peimanmohseni9239 2 роки тому

    Awesome!

    • @WrathofMath
      @WrathofMath  2 роки тому +1

      Thanks, Peiman! If you're looking for more graph theory, check out my playlist! ua-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html

    • @peimanmohseni9239
      @peimanmohseni9239 2 роки тому

      @@WrathofMath Thanks a lot for making these videos. Would you mind adding one on Konig-Egervary theorem and its proof?

  • @ugashinipreethi2620
    @ugashinipreethi2620 2 роки тому

    Does matching ( maximal, maximum , perfect) exist for graphs with self loops? That is if we consider the degree of the loop as 1 ?

    • @WrathofMath
      @WrathofMath  2 роки тому

      Thanks for watching and the question! I'd think a loop would have no impact whatsoever on matchings, since it couldn't possibly be included in one, as matchings should induce bipartite subgraphs which a loop would prevent. That said, I've never looked into this topic specifically, a search may yield results that have found it useful to treat this subject differently.

  • @BenTJacobson
    @BenTJacobson 4 роки тому

    Can you do a video on generating functions? Personally, I'd like to see how they can be used to solve recurrence relations and get the nth term without iteration.

    • @user-qx8xr1sl2r
      @user-qx8xr1sl2r 3 роки тому +1

      maybe you could read Concrete Mathematic by Knuth in chapter 7, it will help you a lot!

  • @benedettafrancesconi1455
    @benedettafrancesconi1455 4 роки тому

    Hi! Do you have any lesson regarding linear programming?

  • @muddassirghoorun4322
    @muddassirghoorun4322 3 роки тому

    Great video. Love your chess board!

    • @WrathofMath
      @WrathofMath  3 роки тому

      Thank you, Muddassir! The chess board has been replaced by holiday decor for the new lessons coming out this month, but it will be back for 2021 haha!