{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:44EQ24YD6IEAA56BY4SZYZSCBU","short_pith_number":"pith:44EQ24YD","schema_version":"1.0","canonical_sha256":"e7090d7303f2080077c1c7259c66420d064fea945a4a7f45d6c7a38076e3507a","source":{"kind":"arxiv","id":"1311.1707","version":1},"attestation_state":"computed","paper":{"title":"The probabilistic approach to limited packings in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Andrei Gagarin, Vadim Zverovich","submitted_at":"2013-11-07T15:02:40Z","abstract_excerpt":"We consider (closed neighbourhood) packings and their generalization in graphs. A vertex set X in a graph G is a k-limited packing if for any vertex $v\\in V(G)$, $\\left|N[v] \\cap X\\right| \\le k$, where N[v] is the closed neighbourhood of v. The k-limited packing number $L_k(G)$ of a graph G is the largest size of a k-limited packing in G. Limited packing problems can be considered as secure facility location problems in networks.\n  In this paper, we develop a new probabilistic approach to limited packings in graphs, resulting in lower bounds for the k-limited packing number and a randomized al"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1311.1707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-11-07T15:02:40Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"dd05f24f6f9297cd017157f33f7adbf485f7919372755420e85f0bc03c080d41","abstract_canon_sha256":"fe7ae99a9e25fcaccd9871203d1315348afe636b95497eb63891dad43ab53500"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:41.982771Z","signature_b64":"kjNqD+m/Y+fDW9gTkITjJe7U6MPd+4Zj/XdP/BgR+EtV5+zJuEBzb9vrym1ZeVjmAQm/Y0gpCg6EOt/5PQP+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7090d7303f2080077c1c7259c66420d064fea945a4a7f45d6c7a38076e3507a","last_reissued_at":"2026-05-18T02:09:41.982064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:41.982064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The probabilistic approach to limited packings in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Andrei Gagarin, Vadim Zverovich","submitted_at":"2013-11-07T15:02:40Z","abstract_excerpt":"We consider (closed neighbourhood) packings and their generalization in graphs. A vertex set X in a graph G is a k-limited packing if for any vertex $v\\in V(G)$, $\\left|N[v] \\cap X\\right| \\le k$, where N[v] is the closed neighbourhood of v. The k-limited packing number $L_k(G)$ of a graph G is the largest size of a k-limited packing in G. Limited packing problems can be considered as secure facility location problems in networks.\n  In this paper, we develop a new probabilistic approach to limited packings in graphs, resulting in lower bounds for the k-limited packing number and a randomized al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1707","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1311.1707","created_at":"2026-05-18T02:09:41.982166+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.1707v1","created_at":"2026-05-18T02:09:41.982166+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1707","created_at":"2026-05-18T02:09:41.982166+00:00"},{"alias_kind":"pith_short_12","alias_value":"44EQ24YD6IEA","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"44EQ24YD6IEAA56B","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"44EQ24YD","created_at":"2026-05-18T12:27:32.513160+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/44EQ24YD6IEAA56BY4SZYZSCBU","json":"https://pith.science/pith/44EQ24YD6IEAA56BY4SZYZSCBU.json","graph_json":"https://pith.science/api/pith-number/44EQ24YD6IEAA56BY4SZYZSCBU/graph.json","events_json":"https://pith.science/api/pith-number/44EQ24YD6IEAA56BY4SZYZSCBU/events.json","paper":"https://pith.science/paper/44EQ24YD"},"agent_actions":{"view_html":"https://pith.science/pith/44EQ24YD6IEAA56BY4SZYZSCBU","download_json":"https://pith.science/pith/44EQ24YD6IEAA56BY4SZYZSCBU.json","view_paper":"https://pith.science/paper/44EQ24YD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.1707&json=true","fetch_graph":"https://pith.science/api/pith-number/44EQ24YD6IEAA56BY4SZYZSCBU/graph.json","fetch_events":"https://pith.science/api/pith-number/44EQ24YD6IEAA56BY4SZYZSCBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/44EQ24YD6IEAA56BY4SZYZSCBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/44EQ24YD6IEAA56BY4SZYZSCBU/action/storage_attestation","attest_author":"https://pith.science/pith/44EQ24YD6IEAA56BY4SZYZSCBU/action/author_attestation","sign_citation":"https://pith.science/pith/44EQ24YD6IEAA56BY4SZYZSCBU/action/citation_signature","submit_replication":"https://pith.science/pith/44EQ24YD6IEAA56BY4SZYZSCBU/action/replication_record"}},"created_at":"2026-05-18T02:09:41.982166+00:00","updated_at":"2026-05-18T02:09:41.982166+00:00"}