A linear-time algorithm for generating auxiliary subgraphs for the 3-edge-connected components of a connected multigraph is presented. The algorithm uses an innovative graph contraction operation and makes only one pass over the graph. By contrast, the previously best-known algorithms make multiple passes over the graph to decompose it into its 2-edge-connected components or 2-vertex-connected components, then its 3-edge-connected components or 3-vertex-connected components, and then construct a cactus representation for the 2-cuts to generate the auxiliary subgraphs for the 3-edge-connected components.

翻译：本文提出了一种线性时间算法，用于生成连通多重图的3边连通分量的辅助子图。该算法采用了一种创新的图收缩操作，仅需对图进行一次遍历。相比之下，先前最著名的算法需要对图进行多次遍历：先将其分解为2边连通分量或2顶点连通分量，再分解为3边连通分量或3顶点连通分量，然后为2割构造仙人掌表示，最后才生成3边连通分量的辅助子图。