{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:WY52B25FFT3GIPXADYQSCX3QWB","short_pith_number":"pith:WY52B25F","schema_version":"1.0","canonical_sha256":"b63ba0eba52cf6643ee01e21215f70b065c0b0ff47bce9e12dc3066813da5cae","source":{"kind":"arxiv","id":"2106.11130","version":1},"attestation_state":"computed","paper":{"title":"Long induced paths in a configuration model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Gabriel Faraud, Laurent M\\'enard, Nathana\\\"el Enriquez, Nathan Noiry","submitted_at":"2021-06-21T14:09:30Z","abstract_excerpt":"In an article published in 1987 in Combinatorica \\cite{MR918397}, Frieze and Jackson established a lower bound on the length of the longest induced path (and cycle) in a sparse random graph. Their bound is obtained through a rough analysis of a greedy algorithm. In the present work, we provide a sharp asymptotic for the length of the induced path constructed by their algorithm. To this end, we introduce an alternative algorithm that builds the same induced path and whose analysis falls into the framework of a previous work by the authors on depth-first exploration of a configuration model \\cit"},"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":"2106.11130","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-06-21T14:09:30Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b7c43168eabaf4bf9cc791f04df7e1bffce627f1f82e727e2a5e1dde4dcb01e7","abstract_canon_sha256":"e543917b5b4e18c7f20f360283a6e0fdb7b238b82e6d495e610720188814b37d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:50:56.981894Z","signature_b64":"vq5U9zm29skPu5e3zwrXfbbO9Zwybzi/NgYIVVPw1Oo00DKRySwS6AdKkWoZ6qoMsFecCQ24MOy4wOrciWpvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b63ba0eba52cf6643ee01e21215f70b065c0b0ff47bce9e12dc3066813da5cae","last_reissued_at":"2026-07-05T02:50:56.981505Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:50:56.981505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long induced paths in a configuration model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Gabriel Faraud, Laurent M\\'enard, Nathana\\\"el Enriquez, Nathan Noiry","submitted_at":"2021-06-21T14:09:30Z","abstract_excerpt":"In an article published in 1987 in Combinatorica \\cite{MR918397}, Frieze and Jackson established a lower bound on the length of the longest induced path (and cycle) in a sparse random graph. Their bound is obtained through a rough analysis of a greedy algorithm. In the present work, we provide a sharp asymptotic for the length of the induced path constructed by their algorithm. To this end, we introduce an alternative algorithm that builds the same induced path and whose analysis falls into the framework of a previous work by the authors on depth-first exploration of a configuration model \\cit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.11130","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.11130/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2106.11130","created_at":"2026-07-05T02:50:56.981562+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.11130v1","created_at":"2026-07-05T02:50:56.981562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.11130","created_at":"2026-07-05T02:50:56.981562+00:00"},{"alias_kind":"pith_short_12","alias_value":"WY52B25FFT3G","created_at":"2026-07-05T02:50:56.981562+00:00"},{"alias_kind":"pith_short_16","alias_value":"WY52B25FFT3GIPXA","created_at":"2026-07-05T02:50:56.981562+00:00"},{"alias_kind":"pith_short_8","alias_value":"WY52B25F","created_at":"2026-07-05T02:50:56.981562+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.23384","citing_title":"A large hole in pseudo-random graphs","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WY52B25FFT3GIPXADYQSCX3QWB","json":"https://pith.science/pith/WY52B25FFT3GIPXADYQSCX3QWB.json","graph_json":"https://pith.science/api/pith-number/WY52B25FFT3GIPXADYQSCX3QWB/graph.json","events_json":"https://pith.science/api/pith-number/WY52B25FFT3GIPXADYQSCX3QWB/events.json","paper":"https://pith.science/paper/WY52B25F"},"agent_actions":{"view_html":"https://pith.science/pith/WY52B25FFT3GIPXADYQSCX3QWB","download_json":"https://pith.science/pith/WY52B25FFT3GIPXADYQSCX3QWB.json","view_paper":"https://pith.science/paper/WY52B25F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.11130&json=true","fetch_graph":"https://pith.science/api/pith-number/WY52B25FFT3GIPXADYQSCX3QWB/graph.json","fetch_events":"https://pith.science/api/pith-number/WY52B25FFT3GIPXADYQSCX3QWB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WY52B25FFT3GIPXADYQSCX3QWB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WY52B25FFT3GIPXADYQSCX3QWB/action/storage_attestation","attest_author":"https://pith.science/pith/WY52B25FFT3GIPXADYQSCX3QWB/action/author_attestation","sign_citation":"https://pith.science/pith/WY52B25FFT3GIPXADYQSCX3QWB/action/citation_signature","submit_replication":"https://pith.science/pith/WY52B25FFT3GIPXADYQSCX3QWB/action/replication_record"}},"created_at":"2026-07-05T02:50:56.981562+00:00","updated_at":"2026-07-05T02:50:56.981562+00:00"}