I've been asked to give an example of a graph in which each vertex has at least degree 2017 and which is not 2-connected.
At first, I was thinking about a fully-connected graph on 2017 vertices which is 2016-connected. But this answer is wrong since any n-connected graph is also n-1, n-2, ..., 1-connected.
Could somebody give me a hint? Thanks.
Take two copies of $K_{2018}$ and join them by one edge.