{"paper":{"title":"Decremental SPQR-trees for Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Adam Karczmarz, Eva Rotenberg, Giuseppe F. Italiano, Jacob Holm, Jakub {\\L}\\k{a}cki","submitted_at":"2018-06-28T05:17:44Z","abstract_excerpt":"We present a decremental data structure for maintaining the SPQR-tree of a planar graph subject to edge contractions and deletions. The update time, amortized over $\\Omega(n)$ operations, is $O(\\log^2 n)$.\n  Via SPQR-trees, we give a decremental data structure for maintaining $3$-vertex connectivity in planar graphs. It answers queries in $O(1)$ time and processes edge deletions and contractions in $O(\\log^2 n)$ amortized time. This is an exponential improvement over the previous best bound of $O(\\sqrt{n}\\,)$ that has stood for over 20 years. In addition, the previous data structures only supp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10772","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}