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Abstract
Have a look at the following drawing:
The problem C is to colour the vertices 1, ..., 5 with one of two available colours, in such a way that vertices of the same edge have different colours. The answer is simple, but think of the same problem, denoted by C+, to colour a complex graph with 1000 vertices, 10000 edges and a palette of 7 colours. The search for efficient methods of solving a problem like C+, so either finding an explicit solution or proving that no solution exists, forms a central challenge for contemporary mathematics.
