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> Let $G$ be a 2-connected graph, $G$ is minimally 2-connected if for any $e \in E(G)$, $G-e$ is not 2-connected. For each number $n$, construct a minimally 2-connected graph with a vertex of degree at least $n$.
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I tried using the bipartite and similar graphs to construct such examples. But I never succeeded in finding them. Is there a clever way to construct such graphs? Thanks.