Four Colour Problem
Main references on the Internet are:
 The four colour theorem
 The Four Color Theorem
Instead of reiterating the theoretical work on this subject, I have succeeded
in devising a rather general computer program, which
attempts to do Four Colouring on Bit MaPs (BMP files)
in practice.
The final
algorithm is optimal, in the sense that it uses the minimum number of
colors. Most of the time 4 of them are required (according to the Four Color
Theorem); see below at 'Best Results so far'. But there are
several other goodies in the program as well (and I find them equally important
at least):
 An algorithm which generates closed and oriented Contour lines, for
quite arbitrary Black and White Bitmaps
 An algorithm for classifying all of the Countries, especially those with
Enclaves inside (also with a robust definition of the "inside" notion)
 Determining the Neighbours of a Country, treated like solving a Radiative
Heat Transfer problem in 2D, where white pixels are the "opaque" medium
 Euclid's GCD (Greatest Common Divisor) Algorithm, for obtaining a discrete
approximation to straight linesofsight through the B/W medium
Best practice: only download the latest version
Don't forget to download some BitMaPs as well
Disclaimer: anything FREE comes without guarantee!
But, in the latter case, please drop some notification at the author's
Email adress.
Country Maps
(*) Nederlandse Informatica Olympiade 1999 opgave 3
[ 1 ] ,
[ 2 ] ,
[ 3 ] ,
[ 4 ] ,
[ 5 ] ,
[ 6 ] ,
[ 7 ] ,
[ 8 ] ,
[ 9 ] ,
[ 10 ] ,
[ 11 ] ,
[ 12 ] ,
[ 13 ] ,
[ 14 ] ,
[ 15 ] ,
[ 16 ] ,
[ 17 ] ,
[ 18 ] ,
[ 19 ] .
Best Results so far
Country Map  # colours

Afrika.bmp  4

Boxville.bmp  4

Bump.bmp  3

col0.bmp  2

Islands.bmp  2

Popdale.bmp  4

Swirl.bmp  2

map_tyler.bmp  4

map_tara.bmp  4

map_miker.bmp  4

map_mike.bmp  4

map_jummy.bmp  4

map_eric.bmp  4

map_amanda2.bmp  4

map_amanda1.bmp  4

nio1.bmp  4

nio2.bmp  4

Wheel1.bmp  4

Wheel2.bmp  3

Country Map # Colorings Calculations

Afrika.bmp = 1.572.480 / (4!)^2 = 2.730
Boxville.bmp = 2.998.080 / (4!)^2 = 5.205
Bump.bmp = 36 (see details)
Col0.bmp = 2
Islands.bmp = 2 (same details)
Map_Eric.bmp = 144 (same details)
Map_Mike.bmp = 62.208 / (4!)^2 = 108
Map_Tara.bmp > 34.400.000 (combinatorial explosion)
Popdale.bmp > 22.500.000 (combinatorial explosion)
Swirl.bmp = 2
nio1.bmp = 49.152 / (4!) = 2048 = 2^11
nio2.bmp = 480 / (4!) = 20
Wheel1.bmp = 8.184 / (4!) = 341
Wheel2.bmp = 6 (same details)
Additional maps from a 'sci.math'
poster :
blueprint (not found) & coloured
;
blueprint (not found) & coloured
;
blueprint &
coloured
;
blueprint &
coloured
;
blueprint &
coloured
;
blueprint &
coloured , also found
here.