I encountered a problem when studying for my finals. I would appreciate it if you guys could give me some tips on how to solve this problem.
Let $G$ be a graph of order $n \geq 2$. Assume $G$ has no isolated vertices. Let $M$ be a maximum matching of $G$ and $x$ the number of vertices in $G$ that are not $M$-saturated.
Show that $x \leq |M|(\Delta (G)-1)$.
Thanks for the help!