Four color fun
The four color theorem says no map requires more than four colors, but some can require fewer.
- The first illustration shows a 12-region map that only requires two colors.
- In the second illustration, you erase a boundary to create an 11-region map that requires three colors.
- In the last, you erase 5 more boundaries to create a 6-region map that requires four colors.
Begin with a map that can be two-colored.
Erase one or more boundaries to create a new map that requires three colors.
Again erase one or more boundaries to create a final map that requires four colors.
What is the minimum number of regions in the starting map for this to be possible?
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1 solution
A lower bound on the answer is 6. This is possible if only one border is erased each time. Here is one solution that does achieve 6 .