Graph coloring is deceptively simple. The idea of coloring a graph is very straightforward, and it seems as if it should be relatively straightforward to find a coloring. It turns out to not be – in fact, it’s extremely difficult. A simple algorithm for graph coloring is easy to describe, but potentially extremely expensive to run. In terms of computational complexity – the measure that we computer scientists use to describe how hard it is to compute a solution to a problem – it’s actually NP-hard.
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