isthmus-free graph

A bridgeless graph, also called an isthmus-free graph, is a graph that contains no graph bridges. Examples of bridgeless graphs include complete graphs on n>2 nodes, cycle graphs, the diamond graph, empty graphs, and the singleton graph. Connected bridgeless graphs are 2-edge connected and can be tested for in the Wolfram Language using KEdgeConnectedGraphQ[g, 2] or EdgeConnectivity[g] >1. A graph that is not bridgeless is said to be bridged. The numbers of simple bridgeless graphs on n = 1, 2, ... vertices are 1, 1, 2, 5, 16, 77, 582, 8002, ... (OEIS A263914).

bridged graph | cycle double cover conjecture | graph bridge | k-edge-connected graph