A simple certifying algorithm for 3-edge-connectivity

02/11/2020

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by   Yung H. Tsin, et al.

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A linear-time certifying algorithm for 3-edge-connectivity is presented. Given an 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 at the same time generates a construction sequence for each connected component as well as the bridges and a cactus representation of the cut-pairs in G. All of these are done by making only one pass over G using an innovative graph contraction technique. Moreover, the graph need not be 2-edge-connected.