@inproceedings{1f2fd1c6b8f243f5b9a6632c1d694a79,
title = "Good r-Divisions Imply Optimal Amortized Decremental Biconnectivity",
abstract = "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(m) total time while answering queries to pairwise biconnectivity in worst-case O(1) time. In case the vertices are not biconnected, the data structure can return a cutvertex separating them in worst-case O(1) time. 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.",
keywords = "Dynamic graphs, 2-connectivity, Graph minors, r-divisions, Graph separators",
author = "Jacob Holm and Eva Rotenberg",
year = "2021",
doi = "10.4230/LIPIcs.STACS.2021.42",
language = "English",
isbn = "9783959771801",
series = "Leibniz International Proceedings in Informatics",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
booktitle = "Proceedings of 38th International Symposium on Theoretical Aspects of Computer Science",
note = "38<sup>th</sup> International Symposium on Theoretical Aspects of Computer Science, STACS 2021 ; Conference date: 16-03-2021 Through 19-03-2021",
}