Abstract
A linear-time certifying algorithm for 3-edge-connectivity is presented. Given a connected undirected graph G, if G is 3-edge-connected, the algorithm generates a construction sequence as a positive certificate for G. Otherwise, the algorithm decomposes G into its 3-edge-connected components and generates a construction sequence for each of them as well as the bridges and a cactus representation of the cut-pairs in G as negative certificates. All of these are done by making only one pass over G using an innovative graph contraction technique. Moreover, the graph needs not be 2-edge-connected. The currently best-known algorithm is more complicated as it makes multiple passes over G and uses involved reduction and perturbation techniques rather than just basic graph-theoretic techniques.
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