{"paper":{"title":"Generalized Cores","license":"","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"M. Zaver\\v{s}nik, V. Batagelj","submitted_at":"2002-02-28T17:40:25Z","abstract_excerpt":"Cores are, besides connectivity components, one among few concepts that provides us with efficient decompositions of large graphs and networks.\n  In the paper a generalization of the notion of core of a graph based on vertex property function is presented. It is shown that for the local monotone vertex property functions the corresponding cores can be determined in $O(m \\max (\\Delta, \\log n))$ time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0202039","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"}