Bridge (graph theory)

A graph with 16 vertices and six bridges (highlighted in red)
An undirected connected graph with no bridge edges

In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components.[1] Equivalently, an edge is a bridge if and only if it is not contained in any cycle. For a connected graph, a bridge can uniquely determine a cut. A graph is said to be bridgeless or isthmus-free if it contains no bridges.

This type of bridge should be distinguished from an unrelated meaning of "bridge" in graph theory, a subgraph separated from the rest of the graph by a specified subset of vertices; see bridge in the Glossary of graph theory.

  1. ^ Bollobás, Béla (1998), Modern Graph Theory, Graduate Texts in Mathematics, vol. 184, New York: Springer-Verlag, p. 6, doi:10.1007/978-1-4612-0619-4, ISBN 0-387-98488-7, MR 1633290.