A simple test on 2-vertex- and 2-edge-connectivity

Testing a graph on 2-vertex- and 2-edge-connectivity are two fundamental algorithmic graph problems. For both problems, different linear-time algorithms with simple implementations are known. Here, an even simpler linear-time algorithm is presented that computes a structure from which both the 2-vertex- and 2-edge-connectivity of a graph can be easily “read off ”. The algorithm computes all bridges and cut vertices of the input graph in the same time.

► A very simple linear-time test on the 2-vertex- and 2-edge-connectivity of a graph. ► Computes a structure from which both the 2-vertex- and 2-edge-connectivity of a graph can be easily “read off”. ► Suitable for teaching in undergraduate courses. ► Computes all bridges and cut vertices.