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Good r-divisions Imply Optimal Amortised Decremental Biconnectivity [article]

Jacob Holm, Eva Rotenberg
2019 arXiv   pre-print
As an immediate consequence, this gives optimal amortized decremental biconnectivity, 2-edge connectivity, and connectivity for large classes of graphs, including planar graphs and other minor free graphs  ...  We present a data structure that, given a graph G of n vertices and m edges, and a suitable pair of nested r-divisions of G, preprocesses G in O(m+n) time and handles any series of edge-deletions in O(  ...  Combined with Theorem 1, we thus obtain decremental biconnectivity with optimal worst-case query-time and amortized optimal update time. Proof.  ... 
arXiv:1808.02568v2 fatcat:cgagyqobrbfvdjzj42potvcdnm