Cuts and Connectivity

@inproceedings{Wallis2000CutsAC,
  title={Cuts and Connectivity},
  author={Walter D. Wallis},
  year={2000}
}
Among connected graphs, some are connected so slightly that removal of a single vertex or edge will disconnect them. Such vertices and edges are quite important. A vertex x is called a cutpoint in G if G — x contains more components than G does; in particular if G is connected, then a cutpoint is a vertex x such that G — x is disconnected. Similarly a bridge (or cut-edge) is an edge whose deletion increases the number of components.