Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 145 / 2 / f / Solution

A proper colouring using exactly $k$ colours first partitions the vertices into $k$ nonempty independent colour classes and then injectively assigns $k$ of the $x$ named colours to those classes. These choices numberSumming over $k$ counts every proper colouring exactly once; the expression is the chromatic polynomial ${\chi }_G(x)$.

Solved by gpt-5.6-sol high.