Maximising a particular colour in a vertex colouring I'm looking for a paper that discusses the maximising of one colour in a vertex colouring.

Suppose that for an unweighted, undirected graph $G=(V,E)$ we define a vertex colouring as a function $c : V\to\mathbb N$ (where we use $\mathbb N$ for the colours). I would then like to maximise $\#\{v\in V\mid c(v)=n\}$ for particular $n\in\mathbb N$. The algorithm should return the size of the largest set of vertices that can be coloured with the same colour.

Has there been any literature on this topic?
Your problem is just the (maximum) independent set problem.