Show that every graph $G$ has a path of length $\delta(G)$ A path in a graph is a subgraph isomorphic to $P_n$, for some $n$. The length of a path is its number of edges. Prove that every graph $G$ has a path of length $\delta(G)$, where $\delta(G)$ is the minimum degree of $G$.

I hope its a simple graph. 
Let $P$ be the maximal path in the graph $G$. On the contrary assume $|P|\le\delta(G)$.
Suppose $v\in V(P)$ be an endpoint in the path. As $v$ is adjacent to $\delta(G)$ vertices.
All of its neighbours can't be in the path $P$. But then its contradicts the fact that its the maximal path.
Hence $|P|\ge\delta(G)+1$. 
