{"paper":{"title":"Dynamic domination and independence in sparse graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anna Zych-Pawlewicz, Bart{\\l}omiej Bosek, Micha{\\l} Pilipczuk, Wojciech Nadara","submitted_at":"2026-07-24T15:10:32Z","abstract_excerpt":"Let $\\mathscr{C}$ be a class of graphs of bounded expansion and $r,k\\in \\mathbb{N}$ be fixed. We give a dynamic data structure that for a given dynamic graph $G$, updated by edge insertions and deletions subject to the promise that $G\\in \\mathscr{C}$ at all times, maintains the answer to the following two queries: (a) Does $G$ contain a distance-$r$ dominating set of size $k$? (b) Does $G$ contain a distance-$r$ independent set of size $k$? The data structure is randomized with error probability bounded by $\\varepsilon$, for a parameter $\\varepsilon>0$ fixed upon the initialization. The amorti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22384","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.22384/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}