  A multigraph is exactly k-edge-connected if there are exactly k edge-disjoint
paths between any pair of vertices. We characterize the class of exactly
3-edge-connected graphs, giving a synthesis involving two operations by which
every exactly 3-edge-connected multigraph can be generated. Slightly modified
syntheses give the planar exactly 3-edge-connected graphs and the exactly
3-edge-connected graphs with the fewest possible edges.
