Show that an acyclic graph has a vertex of degree at most one. Prove that a tree (that is, a connected acyclic graph) of order $n$ has size $n-1$, and deduce that every connected graph of order $n$ and size $n-1$ is a tree.

Let $T$ be a tree of order $t$. Show that if $G$ is a graph with $\delta(G) \geqslant t-1$ then $T$ is a subgraph of $G$, but that this need not happen if $\delta(G) \geqslant t-2$.