[martinjacobd]

> Michigan, with its separate upper peninsula, doesn’t actually prevent the U.S. map from being four-colorable, but it could, mathematically.

Couldn't you always "connect" the upper and lower parts of Michigan, four color the map that way, and then erase the line you drew? I'm having trouble seeing why Michigan (or Michigan-like states) could ever pose a problem as it seems to be solvable easily.

Does the hole caused by Lake Michigan pose a problem? I see the number of colors grows if you have a torus, but Lake Michigan (or its equivalent) is a 2D hole not a 3D one.

[well1912]

If you consider water to be included in the four colors, then connecting the upper and lower peninsulas through the water does nothing but move the problem between the Michigan segments to be a problem between the water segments.

If you connect Michigan between the water and the land, then you'll have to account for the fact that the water on one side and land on the other can be colored the same during the connection but _can't_ after the connection is erased.

[martinjacobd]

Okay I see what you're saying. I was considering water as a hole in the map not a color, but that does make sense.