Graph Theory 7: Five Color Theorem

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  • เผยแพร่เมื่อ 19 มิ.ย. 2024
  • An introduction to the four color map theorem and proof of the five color theorem.

ความคิดเห็น • 30

  • @commandotaco
    @commandotaco 4 ปีที่แล้ว +5

    This is the most excellent explanation of this theorem I have ever seen. Very well done!

  • @cafeinst
    @cafeinst 3 ปีที่แล้ว +5

    That's it? I always thought the proof of the 5CC was more complicated. Thank you for setting me straight.

  • @abhijithsreeraj
    @abhijithsreeraj 3 ปีที่แล้ว +6

    This was amazing! Thank you for making this so easy to understand.

  • @minchuncho1710
    @minchuncho1710 3 ปีที่แล้ว +2

    Your teaching is colorful and detailed. Thank you so much for making it easier to understand.

  • @syremusic_
    @syremusic_ 3 ปีที่แล้ว

    Thank you so much. What a clear, beautifully presented explanation.

  • @aastharanibansal9833
    @aastharanibansal9833 4 ปีที่แล้ว

    This was extremely lovely as well as lively.

  • @dr.anjusunildahiya8138
    @dr.anjusunildahiya8138 2 ปีที่แล้ว

    Beautifully explained... Amazing Thank u so much ❤

  • @kingshukdutta2064
    @kingshukdutta2064 4 ปีที่แล้ว +7

    The proof was a really brilliant one!

  • @Micro-Digressions
    @Micro-Digressions 3 ปีที่แล้ว +12

    It's Idaho, not Iowa.

  • @christopherwalsh3101
    @christopherwalsh3101 3 ปีที่แล้ว +7

    why cant all the countries come together, regardless of their color? :-(

  • @shanmukhchandrayama8508
    @shanmukhchandrayama8508 3 ปีที่แล้ว

    Very cool and simple explanation dude

  • @vipinkp7120
    @vipinkp7120 2 ปีที่แล้ว

    Thankyou for making this clear

  • @ozgunakyuz6887
    @ozgunakyuz6887 3 ปีที่แล้ว

    Great explanation!

  • @aislinnsmith9935
    @aislinnsmith9935 3 ปีที่แล้ว +3

    How do know that when you swap colors in the connected chain you aren't undoing a prior coloring?

  • @sakshishirole9070
    @sakshishirole9070 5 หลายเดือนก่อน

    Amazing explanation

  • @NoOneIsHereRightNow
    @NoOneIsHereRightNow 3 ปีที่แล้ว

    amazinggg thank you soo much

  • @Bharatsingh-fv6xf
    @Bharatsingh-fv6xf 2 ปีที่แล้ว

    Thanks 4 ur lecture video plz. Clarify if we have only one chain and except the middle vertex and the chained vertices all have degree 1 then still we can not hv any free color to color the middle one

  • @AkashKumar-lr6hc
    @AkashKumar-lr6hc ปีที่แล้ว

    Amazing

  • @juheehong7445
    @juheehong7445 2 ปีที่แล้ว +2

    I'm a lil confused still-how can we assume that the chains will always contain two colours (orange and blue, or yellow and pink for eg)? Mightn't things be different if the chains had more colours? Also, why does the cycle of blue and orange vertices (left side) act as a barrier to yellow-pink chain? Couldn't (say) a pink vertex connect to (say) a blue dot as well?

    • @MathatAndrews
      @MathatAndrews  2 ปีที่แล้ว +1

      Great question! Think about it this way: Start with a blue vertex. If it touches any orange vertices, count that as part of the chain. Then if those count any blue vertices, consider that part of the chain. And so on. Now, once you have a blue/orange chain, yellow and pink vertices can connect with it, but no yellow/pink chain can pass *through* it. Does that help?

    • @juheehong7445
      @juheehong7445 2 ปีที่แล้ว

      Thank you so much for such a prompt reply-that makes a lot more sense! So the diagrams you drew are a kind of simplifications that only show the colours we care about. Am I right in understanding that say I have a sequence of blue-yellow-pink-orange connected in a single line, I'd still count that as a blue-orange chain?
      But I don't quite get why no yellow/pink chain can pass through another chain. I don't see why the line you drew at 13:53 is invalid, because wouldn't the graph still be planar?
      Also, if I keep the line from 13:53, and at 13:58 I connect the newest pink dot to the blue dot with an "x" on it, since they're connected through a vertex, isn't that still planar as well? Why isn't this allowed?

  • @UA441
    @UA441 3 ปีที่แล้ว

    thanks

  • @leahj.4404
    @leahj.4404 ปีที่แล้ว +1

    👍👍

  • @zaidazmy
    @zaidazmy ปีที่แล้ว

    little complicated idea. but got it at last

  • @SilverFahrenheit
    @SilverFahrenheit 3 ปีที่แล้ว +1

    Same proof as my graph theory course

    • @MathatAndrews
      @MathatAndrews  3 ปีที่แล้ว +1

      Where are you studying graph theory, if I may ask?

    • @SilverFahrenheit
      @SilverFahrenheit 3 ปีที่แล้ว +2

      Bologna, Italy (unibo)

    • @BjKenklies
      @BjKenklies 3 ปีที่แล้ว +2

      same here, studying bioinformatics in Leipzig, Germany and this series helps me a lot with the upcoming exam!

  • @teqnify63
    @teqnify63 หลายเดือนก่อน

    Idaho 😭

  • @HolahkuTaigiTWFormosanDiplomat
    @HolahkuTaigiTWFormosanDiplomat 3 ปีที่แล้ว

    0.0