Biconnectedness.A graph is biconnectedif every pair of vertices is connected by two vertex-disjoint paths. Two paths between s and t are vertex disjoint if they do not have any internal vertices in common. An articulation pointin a connected graph is a vertex that would disconnect the graph if it (and its incident edges) were removed. Prove that any graph with no articulation points is biconnected. Hint: Given a pair of vertices s and t and a path connecting them, use the fact that none of the vertices on the path are articulation points to construct two disjoint paths connecting s and t.
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