In my studies in graph theory I recently came across the following problem, but first three definitions I use:
A cut vertex $ v $ of an undirected graph $ G $ is a vertex such that $ G-v $ has more connected components than $ G $
A block is an undirected graph which is connected with no cut vertices.
A block of an undirected graph is a subgraph which is itself a block and not properly contained in any other block subgraph.
And here is the question on which I am stuck:
Let $ G=(V,E) $ be a non-empty finite simple undirected graph which is connected and not a block, then $G$ contains at least one block with one cut vertex.
I am quite new to graph theory on this level and I have no idea how to tackle this sort of question, I have no idea and would certainly appreciate all help on this, thanks.