Separator-Based Sparsification II: Edge and Vertex Connectivity

@article{Eppstein1998SeparatorBasedSI,
  title={Separator-Based Sparsification II: Edge and Vertex Connectivity},
  author={David Eppstein and Zvi Galil and Giuseppe F. Italiano and Thomas H. Spencer},
  journal={SIAM J. Comput.},
  year={1998},
  volume={28},
  pages={341-381}
}
We consider the problem of maintaining a dynamic planar graph subject to edge insertions and edge deletions that preserve planarity but that can change the embedding. We describe algorithms and data structures for maintaining information about 2- and 3-vertex-connectivity, and 3- and 4-edge-connectivity in a planar graph in O(n1/2) amortized time per insertion, deletion, or connectivity query. All of the data structures handle insertions that keep the graph planar without regard to any… 
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