Thread: Only 4 are used!

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  1. 05-14-2004 #1
    jlou
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    Glirk Dient's won't work, because two areas are allowed to have the same color if they only touch at a point (the areas may share a vertex point).

    In the top one for JaWiB, the light blue can be changed to dark green.

    In the bottom one, I assume the light blue and the dark blue overlap by more than just a vertex. If so, the red one can be turned yellow (or the yellow can be turned red). If not, then it is like Glirk Dient's comment, and you only need three colors.

    I don't see areas in Zach L.'s picture. How does it apply?
  2. 05-14-2004 #2
    DavidP
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    Zach's is more theoretical. His wont actually work on a single 2d plane, but would require a 3 dimensional representation because he has overlapping lines.
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  3. 05-14-2004 #3
    Zach L.
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    Quote Originally Posted by DavidP
    Zach's is more theoretical. His wont actually work on a single 2d plane, but would require a 3 dimensional representation because he has overlapping lines.
    Precisely!

    jlou, as for the picture, I just decomposed it into the more graph theoretical representation. The maps can be represented as points (the colored areas), with lines connecting them (indicating that the two regions share an edge). The primary motivation for that particular representation is that I have no artistic skill.
  4. 05-15-2004 #4
    Perspective
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    alright, ill take a shot at it.

    *note: black region counts as a region that needs to be coloured. I guess i could have used orange or something
  5. 05-15-2004 #5
    anonytmouse
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    Change the inner black to blue and the outer black to yellow.

    According to this page:
    http://www.math.gatech.edu/~thomas/FC/fourcolor.html
    The next major contribution came from Birkhoff whose work allowed Franklin in 1922 to prove that the four color conjecture is true for maps with at most 25 regions.
    So if you want to 'solve' it maybe you should try using more than 25 regions.
    Last edited by anonytmouse; 05-15-2004 at 09:14 AM.
  6. 05-15-2004 #6
    scrappy
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    hmm.. how about this?
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