Graph Colouring Problem

In the context of the Design and Analysis of Algorithms, the Graph Colouring Problem is a classic problem in graph theory and computer science. Here's a detailed definition:

### Graph Colouring Problem

Definition:
The Graph Colouring Problem is a problem of assigning colours to the vertices of a graph such that no two adjacent vertices share the same colour. The objective is to use the minimum number of colours possible to achieve this.

### Formal Definition:

Given a graph \( G = (V, E) \), where \( V \) is the set of vertices and \( E \) is the set of edges, the task is to assign a colour to each vertex such that:

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