Given a $k$-regular simple graph $G$ of $n$ vertices, show that $\chi(G) \geq n/(n-d)$, where $\chi(G)$ is the chromatic number of $G$.
I'm rather unsure how to start this one, however my initial approach to it was induction on n number of vertices. However unless I'm missing something (most likely) my inductive argument seems to fail as I cannot justify my inductive step (given our IH, how do I progress from there to complete inductive step?). And since it is an inequality I don't think double counting is an applicable approach (although I haven't tried but that is my guess).