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Let δ ≥ 2. Prove that every simple graph G satisfying δmin(G) ≥ δ and containing...

Let δ ≥ 2. Prove that every simple graph G satisfying δmin(G) ≥ δ and
containing no triangles contains a cycle of length at least 2δ.
Prove that this result is sharp by showing that we cannot guarantee the existence of
a cycle of length at least 2δ + 1. Give a counterexample for each δ.

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