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In case the vertices are not biconnected, the data structure can return a cutvertex separating them in worst-case <jats:italic>O<\/jats:italic>(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.<\/jats:p>","DOI":"10.1007\/s00224-024-10181-z","type":"journal-article","created":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T10:02:15Z","timestamp":1719482535000},"page":"1014-1048","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Good r-divisions Imply Optimal Amortized Decremental Biconnectivity"],"prefix":"10.1007","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6997-9251","authenticated-orcid":false,"given":"Jacob","family":"Holm","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5853-7909","authenticated-orcid":false,"given":"Eva","family":"Rotenberg","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,27]]},"reference":[{"key":"10181_CR1","volume-title":"The Design and Analysis of Computer Algorithms","author":"AV Aho","year":"1974","unstructured":"Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms, 1st edn. 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