My problem is as follows:
Let $G$ be a graph. Suppose that $C$ is a vertex covering of $G$ and that $M$ is a matching of $G$. Prove that $|M| \le |C|$. What is the implication of this inequality for a vertex covering $C'$ and a matching $M'$ of $G$ such that $|C'|=|M'|$?
I can obviously show this for specific graphs G, but I'm struggling to form a general proof. Can you please help me with this?
Thanks!