K-colourable graph

Definition

Let $k$ be a natural number. A graph $G$ is $k$-colourable if it has a colouring with the set of colours $\{1, 2, \dots, k\}$.

Remarks

A $k$-colourable graph is also $(k+1)$-colourable. A graph is $2$-colourable if and only if it is bipartite. The complete graph $K_n$ is $k$-colourable if and only if $k \ge n$.

Explanations

L1 human

A graph is $k$-colourable when $k$ colours are enough to colour it properly. A triangle needs three colours, so it is $3$-colourable but not $2$-colourable.