Edge versus vertex connectivity
Task number: 3961
Show that each vertex 2-connected graph is edge 2-connected.
(An edge 2-connected graph is such that after removing any edge remains connected.)
If the graph has a bridge and it is not \( K_2 \), then at least one of the ends of this bridge is adjacent to some other vertex and forms the articulation itself.
Find the smallest graph that is edge 2-connected but not vertex 2-connected.
For any pair of integers \( k \geq l \geq 2 \) construct a graph of edge connectivity \(k\) and vertex connectivity \(l\).