(Solution) - The edge connectivity of an undirected graph is the -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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The edge connectivity of an undirected graph is the minimum number k of edges that must be removed to disconnect the graph. For example, the edge connectivity of a tree is 1, and the edge connectivity of a cyclic chain of vertices is 2. Show how the edge connectivity of an undirected graph G = (V, E) can be determined by running a maximum-flow algorithm on at most |V| flow networks, each having O(V) vertices and O(E) edges.