{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SCZBFHOXNOCTIBW2OTBA42LOLF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1c278f8fb24e925d96938178f115a855182042c6aa2cce18051bcae7219efedb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-04-12T16:53:09Z","title_canon_sha256":"f7bcd180ae7d869a5f4797ce85e0e23dd33e0391c24871a99ab5cbf8e31e6c6e"},"schema_version":"1.0","source":{"id":"2404.08599","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.08599","created_at":"2026-07-05T08:07:24Z"},{"alias_kind":"arxiv_version","alias_value":"2404.08599v1","created_at":"2026-07-05T08:07:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.08599","created_at":"2026-07-05T08:07:24Z"},{"alias_kind":"pith_short_12","alias_value":"SCZBFHOXNOCT","created_at":"2026-07-05T08:07:24Z"},{"alias_kind":"pith_short_16","alias_value":"SCZBFHOXNOCTIBW2","created_at":"2026-07-05T08:07:24Z"},{"alias_kind":"pith_short_8","alias_value":"SCZBFHOX","created_at":"2026-07-05T08:07:24Z"}],"graph_snapshots":[{"event_id":"sha256:e7f51b33db188d66a531b0112ab98f73d11d90d565069cd1129d987990d702e5","target":"graph","created_at":"2026-07-05T08:07:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.08599/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze the computational complexity of the following computational problems called Bounded-Density Edge Deletion and Bounded-Density Vertex Deletion: Given a graph $G$, a budget $k$ and a target density $\\tau_\\rho$, are there $k$ edges ($k$ vertices) whose removal from $G$ results in a graph where the densest subgraph has density at most $\\tau_\\rho$? Here, the density of a graph is the number of its edges divided by the number of its vertices. We prove that both problems are polynomial-time solvable on trees and cliques but are NP-complete on planar bipartite graphs and split graphs. From ","authors_text":"Andr\\'e Nichterlein, Cristina Bazgan, Sofia Vazquez Alferez","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-04-12T16:53:09Z","title":"Destroying Densest Subgraphs is Hard"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.08599","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0a193b77963b33d65acabb21da15cfc81ce990edf80be397c034cfdcf25ab77a","target":"record","created_at":"2026-07-05T08:07:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1c278f8fb24e925d96938178f115a855182042c6aa2cce18051bcae7219efedb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-04-12T16:53:09Z","title_canon_sha256":"f7bcd180ae7d869a5f4797ce85e0e23dd33e0391c24871a99ab5cbf8e31e6c6e"},"schema_version":"1.0","source":{"id":"2404.08599","kind":"arxiv","version":1}},"canonical_sha256":"90b2129dd76b853406da74c20e696e596ba5ef267c19771a3c0f6c813d348522","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90b2129dd76b853406da74c20e696e596ba5ef267c19771a3c0f6c813d348522","first_computed_at":"2026-07-05T08:07:24.047885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:07:24.047885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SRBzRRX1Cdp89+3RbNT9sGdu9y7Jx+sFmfLxU3dGgldPXkEuYCbaBaXxg5rlGrZ4+oKPEVQn60QzbLak8NOQCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:07:24.048402Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.08599","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a193b77963b33d65acabb21da15cfc81ce990edf80be397c034cfdcf25ab77a","sha256:e7f51b33db188d66a531b0112ab98f73d11d90d565069cd1129d987990d702e5"],"state_sha256":"d859ee3f3986e4607f6e228c3c95ad647dca4bc0d29c160ed90ce2e31ab814e3"}