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 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]
A graph that is not bridgeless is said to be bridged.
The numbers of simple bridgeless graphs on , 2, ... vertices are 1, 1, 2, 5, 16, 77, 582, 8002, ...
The numbers of simple connected bridgeless graphs on , 2, ... vertices are 1, 0, 1, 3, 11, 60, 502, 7403 ... (OEIS
See alsoBridged Graph
, Cycle Double Cover Conjecture
, Graph Bridge
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ReferencesSloane, N. J. A. Sequences A007146/M2909 and A263914 in "The On-Line Encyclopedia
of Integer Sequences."
Referenced on Wolfram|AlphaBridgeless Graph
Cite this as:
Weisstein, Eric W. "Bridgeless Graph."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BridgelessGraph.html