Dividing a Graph into Triconnected Components
John E. Hopcroft, Robert Endre Tarjan · SIAM Journal on Computing · 1973
An algorithm for dividing a graph into triconnected components is presented. When implemented on a random access computer, the algorithm requires $O(V + E)$ time and space to analyze a graph with V vertices and E edges. The algorithm is both theoretically optimal to within a constant factor and efficient in practice.