A graph G that becomes disconnected when removing a suitable complete subgraph K, called a vertex cut, is said to be quasiseparable. The two simplest cases are those where K is the null graph (which means that G is disconnected) or K is the singleton graph (which means that G can be disconnected by removing one vertex, called articulation or cut vertex). Under these circumstances, G is called separable. A forest is always separable, since every vertex of degree at least two is an articulation vertex.

articulation vertex | biconnected graph | separable graph | vertex cut