cut arc | cut-edge | graph isthmus

A bridge of a connected graph is a graph edge whose removal disconnects the graph. More generally, a bridge is an edge of a not-necessarily-connected graph G whose removal increases the number of components of G. An edge of a connected graph is a bridge iff it does not lie on any cycle. A bridge therefore cannot be a cycle chord. A bridge is also known as an isthmus, cut-edge, or cut arc. Every edge of a tree is a bridge. A connected cubic graph contains a bridge iff it contains an articulation vertex, i.e., if it is not a biconnected graph. A graph containing one or more bridges is said to be a bridged graph, while a graph containing no bridges is called a bridgeless graph.

articulation vertex | block | bridged graph | bridgeless graph | edge cut | k-edge-connected graph