2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229651A 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.15 pages, 4 figures Submitted to FOCS 2009Combinatorics05C40text