Reducing Edge Connectivity to Vertex Connectivity * Zvi Galil Columbia University, and Tel-Aviv University Giuseppe F . Italian o Columbia University, an d Universit y di Roma, Ital y Abstrac t We show how to reduce edge connectivity to vertex connectivity . Using this reduction, w e obtain a linear-time algorithm for deciding whether an undirected graph is 3-edge-connected , and for computing the 3-edge-connected components of an undirected graph . Introductio n Given an undirected graph G = (V, E), and an integer k > 2, a pair of vertices (u, v) is said t o be k-edge-connected if the removal of any k 1 edges in G leaves u and v connected . This is a n equivalence relationship, and we denote it by - k , i .e ., if a pair of vertices (x, yy is k-edge-connecte d we write x y. The vertices of a graph G are partitioned by this relationship into equivalenc e classes called k-edge-connected components . An edge set E' C E is an edge-cut for vertices x an d y if the removal of all the edges in E' disconnects x and y_ The cardinality of an
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Reducing edge connectivity to vertex connectivity
Galil, Zvi; Italiano, Giuseppe F.
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, Volume 22 (1)
Association for Computing Machinery – Mar 1, 1991
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