{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UKEIVQWRR3CP3ORPPXRLARBHGP","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":"0ed00c43d135208cfbd7f6b83e0330bf691e94fb719a843f525422ccdb6960de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-25T19:43:16Z","title_canon_sha256":"ba61a67e2ae77a3dfe5652638e8c4bfa364592ccfdc5bad2d6b76c441d26ff8a"},"schema_version":"1.0","source":{"id":"1210.6965","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6965","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6965v1","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6965","created_at":"2026-05-18T03:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"UKEIVQWRR3CP","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UKEIVQWRR3CP3ORP","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UKEIVQWR","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:cbfc9ae9ed6df49c35addafc2e37e0fc132fa9ad2bdb427e674d56d35bc74a48","target":"graph","created_at":"2026-05-18T03:42:22Z","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"},"paper":{"abstract_excerpt":"A k-clique covering of a simple graph G, is an edge covering of G by its cliques such that each vertex is contained in at most k cliques. The smallest k for which G admits a k-clique covering is called local clique cover number of G and is denoted by $lcc(G)$. Local clique cover number can be viewed as the local counterpart of the clique cover number which is equal to the minimum total number of cliques covering all edges. In this paper, several aspects of the problem are studied and its relationships to other well-known problems are discussed. Moreover, the local clique cover number of claw-f","authors_text":"Behnaz Omoomi, Ramin Javadi, Zeinab Maleki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-25T19:43:16Z","title":"Local Clique Covering of Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6965","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":"sha256:1f952ed470ac30ee1dbe6c23356190a89be59a8b2ce64abe3a60fdf261ec2400","target":"record","created_at":"2026-05-18T03:42:22Z","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":"0ed00c43d135208cfbd7f6b83e0330bf691e94fb719a843f525422ccdb6960de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-25T19:43:16Z","title_canon_sha256":"ba61a67e2ae77a3dfe5652638e8c4bfa364592ccfdc5bad2d6b76c441d26ff8a"},"schema_version":"1.0","source":{"id":"1210.6965","kind":"arxiv","version":1}},"canonical_sha256":"a2888ac2d18ec4fdba2f7de2b0442733f1524dabdc76d89cab8fd428555345b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2888ac2d18ec4fdba2f7de2b0442733f1524dabdc76d89cab8fd428555345b4","first_computed_at":"2026-05-18T03:42:22.670197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:22.670197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iHvbk2Za9Hd8w/XSvaWD9GkJGMqDqTy4mmyA2ZYnWIUJhUzyj+SSedcssrEbMwgXiYaDl/ceo+5qO38ErEDMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:22.670954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6965","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f952ed470ac30ee1dbe6c23356190a89be59a8b2ce64abe3a60fdf261ec2400","sha256:cbfc9ae9ed6df49c35addafc2e37e0fc132fa9ad2bdb427e674d56d35bc74a48"],"state_sha256":"a006f096abd565723ebfb53af35fcc35b943f12d437ecc9c5aafb28228cca40f"}