{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FWSSRDNZALVVS5OHCC4ALLYMXW","short_pith_number":"pith:FWSSRDNZ","schema_version":"1.0","canonical_sha256":"2da5288db902eb5975c710b805af0cbda749ab0d0366e3c76b7e624676a2c051","source":{"kind":"arxiv","id":"1201.2202","version":2},"attestation_state":"computed","paper":{"title":"Robust Hamiltonicity of Dirac graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Choongbum Lee, Michael Krivelevich","submitted_at":"2012-01-10T22:35:21Z","abstract_excerpt":"A graph is Hamiltonian if it contains a cycle which passes through every vertex of the graph exactly once. A classical theorem of Dirac from 1952 asserts that every graph on $n$ vertices with minimum degree at least $n/2$ is Hamiltonian. We refer to such graphs as Dirac graphs. In this paper we extend Dirac's theorem in two directions and show that Dirac graphs are robustly Hamiltonian in a very strong sense. First, we consider a random subgraph of a Dirac graph obtained by taking each edge independently with probability $p$, and prove that there exists a constant $C$ such that if $p \\ge C \\lo"},"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":"1201.2202","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-10T22:35:21Z","cross_cats_sorted":[],"title_canon_sha256":"1733cdbb7934e764538968647ad3256e1a7320c3df1d57c08a44a179f6537df3","abstract_canon_sha256":"1d37e5f9a2d7b6f16a2ec4918c74bb36bf16feeda6c4cfe48f32dc88fdf82b69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:10.709361Z","signature_b64":"CF0PHVei5+0r90e/70IbYK7DRD87A5zn39+2PJtg9tQ/S3hEwQbHsz23mbE/TQrqZP8KEEgZK32IXqy/RjHDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2da5288db902eb5975c710b805af0cbda749ab0d0366e3c76b7e624676a2c051","last_reissued_at":"2026-05-18T03:45:10.708813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:10.708813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Robust Hamiltonicity of Dirac graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Choongbum Lee, Michael Krivelevich","submitted_at":"2012-01-10T22:35:21Z","abstract_excerpt":"A graph is Hamiltonian if it contains a cycle which passes through every vertex of the graph exactly once. A classical theorem of Dirac from 1952 asserts that every graph on $n$ vertices with minimum degree at least $n/2$ is Hamiltonian. We refer to such graphs as Dirac graphs. In this paper we extend Dirac's theorem in two directions and show that Dirac graphs are robustly Hamiltonian in a very strong sense. First, we consider a random subgraph of a Dirac graph obtained by taking each edge independently with probability $p$, and prove that there exists a constant $C$ such that if $p \\ge C \\lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2202","kind":"arxiv","version":2},"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":"1201.2202","created_at":"2026-05-18T03:45:10.708908+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.2202v2","created_at":"2026-05-18T03:45:10.708908+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2202","created_at":"2026-05-18T03:45:10.708908+00:00"},{"alias_kind":"pith_short_12","alias_value":"FWSSRDNZALVV","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FWSSRDNZALVVS5OH","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FWSSRDNZ","created_at":"2026-05-18T12:27:06.952714+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/FWSSRDNZALVVS5OHCC4ALLYMXW","json":"https://pith.science/pith/FWSSRDNZALVVS5OHCC4ALLYMXW.json","graph_json":"https://pith.science/api/pith-number/FWSSRDNZALVVS5OHCC4ALLYMXW/graph.json","events_json":"https://pith.science/api/pith-number/FWSSRDNZALVVS5OHCC4ALLYMXW/events.json","paper":"https://pith.science/paper/FWSSRDNZ"},"agent_actions":{"view_html":"https://pith.science/pith/FWSSRDNZALVVS5OHCC4ALLYMXW","download_json":"https://pith.science/pith/FWSSRDNZALVVS5OHCC4ALLYMXW.json","view_paper":"https://pith.science/paper/FWSSRDNZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.2202&json=true","fetch_graph":"https://pith.science/api/pith-number/FWSSRDNZALVVS5OHCC4ALLYMXW/graph.json","fetch_events":"https://pith.science/api/pith-number/FWSSRDNZALVVS5OHCC4ALLYMXW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FWSSRDNZALVVS5OHCC4ALLYMXW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FWSSRDNZALVVS5OHCC4ALLYMXW/action/storage_attestation","attest_author":"https://pith.science/pith/FWSSRDNZALVVS5OHCC4ALLYMXW/action/author_attestation","sign_citation":"https://pith.science/pith/FWSSRDNZALVVS5OHCC4ALLYMXW/action/citation_signature","submit_replication":"https://pith.science/pith/FWSSRDNZALVVS5OHCC4ALLYMXW/action/replication_record"}},"created_at":"2026-05-18T03:45:10.708908+00:00","updated_at":"2026-05-18T03:45:10.708908+00:00"}