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A $\textit{simple path}$ (respectively cycle) in a graph is a path (respectively cycle) in which no edge or vertex os repeated. The $length$ of such a path (respectively cycle) is the number of edges in the path (respectively cycle).

Let $G$ be an undirected graph with minimum degree $k \geq 2$.

Show that $G$ contains a simple path of length at least $k$.
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