Four color theorem: new ideas


This is what I want to try:

  • Select an F2, F3  or F4 preferably when it is near an F5 and remove the edge that joins the two faces
    • Analyse also the balance of the Euler’s identity when removing edges, to decide if it is better to choose other couple: F2 near the highest or other possibilities
  • Let Deepmind DQN (or Tensorflow) learn the best approach for selecting faces and remove the edges
    • Controls:
      • The selection of the face and the edge based on the characteristics of the neighbor faces
    • Scope:
      • Avoid the F5 worst case (in the rebuilding phase), when it is necessary to apply the random Kempe’s color switches to solve the impasse

The rule: avoid F5 or at least do not create them.

avoid-f5

  • Remove F2 when near F5 –> Good (will get rid of the F5 and generate an F3)
  • Remove F3 when near F5 –> Good (will get rid of the F5 and generate an F4)
  • Remove F4 when near F5 –> NOT Good (will end up with another F5)
  • Remove F5 when near F5 –> Good (will get rid of the F5 and generate an F6)

Other to avoid:

  • Remove F2 when near F7 –> NOT Good (will end up with another F5)
  • Remove F3 when near F6 –> NOT Good (will end up with another F5)

NOTE:

  • It is also important to check what appens to f3 and f4
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