, Volume 77, Issue 2, pp 309–335 | Cite as

Certifying 3-Edge-Connectivity



We present a certifying algorithm that tests graphs for 3-edge-connectivity; the algorithm works in linear time. If the input graph is not 3-edge-connected, the algorithm returns a 2-edge-cut. If it is 3-edge-connected, it returns a construction sequence that constructs the input graph from the graph with two vertices and three parallel edges using only operations that (obviously) preserve 3-edge-connectivity. Additionally, we show how to compute and certify the 3-edge-connected components and a cactus representation of the 2-cuts in linear time. For 3-vertex-connectivity, we show how to compute the 3-vertex-connected components of a 2-connected graph.


Certifying algorithm Edge connectivity Construction sequence 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Kurt Mehlhorn
    • 1
  • Adrian Neumann
    • 1
  • Jens M. Schmidt
    • 1
  1. 1.Max Planck Institute for InformaticsSaarbrückenGermany

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