ABSTRACT
Some connected graphs can be disconnected by the removal of a single point, called a cutpoint. The fragments of a graph held together by its cutpoints are its blocks. A cutpoint of a graph is one whose removal increases the number of components, and a bridge is such a line. A block of a graph is a maximal nonseparable subgraph. Each line of a graph lies in exactly one of its blocks, as does each point which is not isolated or a cutpoint. Thus in particular, the blocks of a graph partition its lines and its cycles regarded as sets of lines. The chapter presents several equivalent conditions for each of these concepts. There are several intersection graphs derived from a graph G which reflect its structure. The blocks of G correspond to the points of B(G) and two of these points are adjacent whenever the corresponding blocks contain a common cutpoint of G.
