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 $n$.
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.