In the paper On the geographical problem of the Four Colors by Kempe, at the end of page 194, it is stated that
It will readily be seen that we can interchange the colours of the districts in one or miore of the red and green regions without doing so in any others, and the map will still be properly coloured. The same remarks apply to the regions composed of districts of any other pair of colour. Now if a region composed of districts of any pair of colours, say red and green as before, be of either of the forms shown in Figures 3 and 4, it will separate the surface into twvo parts, so that we map be quite certain that no yellow or blue districts in one part can belong, to the same yellow and blue region as any yellow or blue district in the other part
But I'm having trouble understading his argument. I mean as far as I understood, those lines in the figures are the boundaries of regions which contain districs, and if we change the colors of district, say blue and green, in one region only, there will be no problem, but can't a district of blue color in the inner region have a neighbour with green color in the outer region ?
I couldn't figure out how to post an image in a comment, so ...
The map has two red/green regions, A and D. It has two blue/yellow regions, B and C. Region B consists of a single blue district. If green and red were switched in region A, the other regions would be unaffected. Every district in A is adjacent to other districts in A or blue/yellow districts in B or C.
The single district in region B can be blue or yellow.
If we wanted blue/green regions and red/yellow regions instead, there would be a single blue/green region and 4 red/yellow regions.