# block

A subgraph $B$ of a graph $G$ is a block of $G$ if either it is a bridge (together with the vertices incident with the bridge) or else it is a maximal 2-connected subgraph of $G$.

Any two blocks of a graph $G$ have at most one vertex in common. Also, every vertex belonging to at least two blocks is a cutvertex of $G$, and, conversely, every cutvertex belongs to at least two blocks.

Adapted with permission of the author from by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.

Title block Block 2013-03-22 12:32:00 2013-03-22 12:32:00 digitalis (76) digitalis (76) 4 digitalis (76) Definition msc 05C99 Cutvertex Bridge