Greedy colouring by removing independent sets
= Greedy colouring by removing independent sets
{title2=$\chi(G)\leq |V(G)|/r+m$}
If every <vertex> subset of size at least $m$ contains an <independent set> of size $r$, repeatedly colour and remove an $r$-element <independent set> while at least $m$ <vertices> remain. Giving each remaining <vertex> its own colour uses at most $|V|/r+m$ colours.