A simple graph with labelled vertices

It all started with Leonhard Euler and the Bridges of Koenigsberg problem. In that problem the only thing that mattered was the pieces of land that were connected. The exact shape, placing and lengths of the bridges were irrelevant.

Graph Theory is also the area with one of the most common examples of Pure Maths found in school, namely, the Four Colour Theorem.

This question was first posed in 1852, and it wasn't until 1976 that a proof was finally given. Even then there was, and still is, some controversy, because the proof requires a computer to check a large number of sub-cases. These then have to be combined in a clever way - the computer doesn't actually do the proof - but even so, it's not a proof in the traditional sense.

You can read more about the Four Colour Theorem and Graph Theory in general here:

• http://en.wikipedia.org/wiki/Four_color_theorem
• http://en.wikipedia.org/wiki/Graph_theory

Quotation from Tim Berners-Lee