graph coloring Algorithm

Vertex colouring is normally used to introduce graph coloring problems since other colouring problems can be transformed into a vertex colouring case. This is partly pedagogical, and partly because some problems are best study in their non-vertex form, as in the case of edge colouring. The first outcomes about graph colouring deal almost exclusively with planar graphs in the form of the colouring of maps. 

In 1912, George David Birkhoff introduced the chromatic polynomial to study the coloring problems, which was generalized to the Tutte polynomial by Tutte, important structures in algebraic graph theory. While trying to color a map of the counties of England, Francis Guthrie postulated the four color conjecture, note that four colors were sufficient to color the map so that no regions sharing a common border received the same color.

graph coloring source code, pseudocode and analysis