# vertices and edges on a cycle

Show that if a simple graph with at least two vertices is connected and has no cut vertices, then any two vertices lie on a cycle and any two edges lie on a cycle.

I assume if $$G$$ is connected and has no cut vertices, then if we remove any vertex from $$G$$, the remaining graph is still connected. And does that automatically mean any two vertices lie on a cycle and any two edges lie on a cycle?

• What have you tried so far? – jwc845 Nov 19 '18 at 15:37
• @jwc845 So I assume if $G$ is connected and has no cut vertices, then if we remove any vertex from $G$, the remaining graph is still connected. And does that automatically mean any two vertices lie on a cycle and any two edges lie on a cycle? – Thomas Nov 19 '18 at 15:58
• This might help: math.stackexchange.com/questions/3005438/… – Just_a_newbie Nov 24 '18 at 10:44