Here's a little C routine demonstrating the 4-colour theorem: using at most 4 colours, every planar graph can be coloured in such a way that no neighbouring nodes have the same colour.
After compiling, the colouring executable accepts a 0-indexed edge list that labels
each vertex with an integer directly from STDIN. If you want to work with a
more descriptive edge list that uses non-integer labels for each vertex,
run process.py, which will convert your list to integers-only format and
pass it to the colouring routine.
NOTE: This routine only works with connected graphs right now.
By Andrew Kerr kerrand@protonmail.com