6.4.21 Graph theory

Problem: Prove that graph \( G \) is edge biconnected if and only if it can be represented as \( G=G_{0} \cup G_{1} \cup \ldots \cup G_{k} \), where \( G_{0} \) is an arbitrary cycle in the graph \( G \), and \( G_{i}, i>0 \), is either a handle, or a closed handle for the subgraph \( G_{0} \cup G_{1} \cup \ldots \cup G_{i-1} \) of graph \( G \).