Graph Theory Proof Problem(Bipartites graphs) I'm struggling to proof something the Professor gave us. I asked several friends and no one knows what to do. Basically is this:

Prove for every simple bipartite Graph with $n \ge 1$ vertex: $$\delta(G)+\Delta(G)\le n.$$

Professor's Tip: Split you answer in two. First prove the follow: 
If $G$ is simple and bipartite with at least $3$ vertices, $G$ has a vertex $v \in V(G)$ that satisfies at least one of these properties:
• $\Delta(G−v)=\Delta(G)$
• $\delta(G−v)= \delta(G)$
Now, prove by induction on $n$ using these properties.
Guys, I don't know where to start and how to use these information! I checked several books ([West], [Chartrand-Zhang] and [Diestel]) and none of them proved to be useful.
Sorry if my English was bad. Thanks!

I don't know how to prove the tip, but the theorem is trivial.  Suppose the parts are $V_1$ and $V_2$, that $|V_1|=n_1$ and $|V_2|=n_2$, where $n_1+n_2=n$.  We may assume that $n_1\geq n_2$.  
Every vertex in $V_1$ has degree at most $n_2$, and every vertex in $V_2$ has degree at most $n_1.$  Thus $\Delta(G)\leq n_1$, $\delta(G)\leq n_2,$ and the theorem follows. 
