• 3 Posts
  • 41 Comments
Joined 4 years ago
cake
Cake day: May 19th, 2021

help-circle

  • Yeah, the four color problem becomes obvious to the brain if you try to place five territories on a plane (or a sphere) that are all adjacent to each other.

    I think one of the earliest attempts at the 4 color problem proved exactly that (that C5 graph cannot be planar). Search engines are failing me in finding the source on this though.

    But any way, that result is not sufficient to proof the 4-color theorem. A graph doesn’t need to have a C5 subgraph to make it impossible to 4-color. Think of two C4 graphs. Choose one vertex from each- call them A and B. Connect A and B together. Now make a new vertex called C and connect C to every vertex except A and B. The result should be a C5-free graph that cannot be 4-colored.


















  • wisha@lemmy.mltoScience Memes@mander.xyzTough Trolly Choices
    link
    fedilink
    English
    arrow-up
    5
    arrow-down
    1
    ·
    5 months ago

    They have to get smaller to fit the problem statement- if all levers are the same size or have some nonzero minimum size then the full set of levers would be countable!

    Now we play the game again 🤓. I start by removing the levers in the field/scale of view of your microscope’s default orientation.


  • wisha@lemmy.mltoScience Memes@mander.xyzTough Trolly Choices
    link
    fedilink
    English
    arrow-up
    4
    arrow-down
    1
    ·
    5 months ago

    But look at the picture: the levers are not all the same size- they get progressively smaller until (I assume from the ellipsis) they become infinitesimally small. If a cluster has this dense side facing you, then you won’t “see” a lever at all. You would only see a uniform sea of gray or whatever color the levers are. You now have to choose where to zoom in to see your first lever.