{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HAUHP4LBWXFCPDVDEU3BFDSMZF","short_pith_number":"pith:HAUHP4LB","schema_version":"1.0","canonical_sha256":"382877f161b5ca278ea32536128e4cc942814443945b36a4288d71264bb6172d","source":{"kind":"arxiv","id":"1309.0978","version":1},"attestation_state":"computed","paper":{"title":"The four-in-a-tree problem in triangle-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Christophe Picouleau, Nicolas Derhy, Nicolas Trotignon","submitted_at":"2013-09-04T11:10:27Z","abstract_excerpt":"The three-in-a-tree algorithm of Chudnovsky and Seymour decides in time $O(n^4)$ whether three given vertices of a graph belong to an induced tree. Here, we study four-in-a-tree for triangle-free graphs. We give a structural answer to the following question: what does a triangle-free graph look like if no induced tree covers four given vertices? Our main result says that any such graph must have the \"same structure\", in a sense to be defined precisely, as a square or a cube.\n  We provide an $O(nm)$-time algorithm that given a triangle-free graph $G$ together with four vertices outputs either a"},"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":"1309.0978","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-09-04T11:10:27Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"12eb0592ec587de72192944c4ab6d415d3a672274e7c72f1bba91486a6425208","abstract_canon_sha256":"e21880ddb089d4eea74651b362620293a5f7fb6ecc1603e98d91004c1b51f12a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:09.441333Z","signature_b64":"cpfvzLqAcR8C7Kfxh/5PNQdLZ56bUPIuJuq0tVsIoCA0p147dXf9Dsw/Ghe7rYJBueoZFQ0JRQYfi7v6ILM7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"382877f161b5ca278ea32536128e4cc942814443945b36a4288d71264bb6172d","last_reissued_at":"2026-05-18T03:14:09.440715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:09.440715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The four-in-a-tree problem in triangle-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Christophe Picouleau, Nicolas Derhy, Nicolas Trotignon","submitted_at":"2013-09-04T11:10:27Z","abstract_excerpt":"The three-in-a-tree algorithm of Chudnovsky and Seymour decides in time $O(n^4)$ whether three given vertices of a graph belong to an induced tree. Here, we study four-in-a-tree for triangle-free graphs. We give a structural answer to the following question: what does a triangle-free graph look like if no induced tree covers four given vertices? Our main result says that any such graph must have the \"same structure\", in a sense to be defined precisely, as a square or a cube.\n  We provide an $O(nm)$-time algorithm that given a triangle-free graph $G$ together with four vertices outputs either a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0978","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":"1309.0978","created_at":"2026-05-18T03:14:09.440839+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.0978v1","created_at":"2026-05-18T03:14:09.440839+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0978","created_at":"2026-05-18T03:14:09.440839+00:00"},{"alias_kind":"pith_short_12","alias_value":"HAUHP4LBWXFC","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HAUHP4LBWXFCPDVD","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HAUHP4LB","created_at":"2026-05-18T12:27:46.883200+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/HAUHP4LBWXFCPDVDEU3BFDSMZF","json":"https://pith.science/pith/HAUHP4LBWXFCPDVDEU3BFDSMZF.json","graph_json":"https://pith.science/api/pith-number/HAUHP4LBWXFCPDVDEU3BFDSMZF/graph.json","events_json":"https://pith.science/api/pith-number/HAUHP4LBWXFCPDVDEU3BFDSMZF/events.json","paper":"https://pith.science/paper/HAUHP4LB"},"agent_actions":{"view_html":"https://pith.science/pith/HAUHP4LBWXFCPDVDEU3BFDSMZF","download_json":"https://pith.science/pith/HAUHP4LBWXFCPDVDEU3BFDSMZF.json","view_paper":"https://pith.science/paper/HAUHP4LB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.0978&json=true","fetch_graph":"https://pith.science/api/pith-number/HAUHP4LBWXFCPDVDEU3BFDSMZF/graph.json","fetch_events":"https://pith.science/api/pith-number/HAUHP4LBWXFCPDVDEU3BFDSMZF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HAUHP4LBWXFCPDVDEU3BFDSMZF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HAUHP4LBWXFCPDVDEU3BFDSMZF/action/storage_attestation","attest_author":"https://pith.science/pith/HAUHP4LBWXFCPDVDEU3BFDSMZF/action/author_attestation","sign_citation":"https://pith.science/pith/HAUHP4LBWXFCPDVDEU3BFDSMZF/action/citation_signature","submit_replication":"https://pith.science/pith/HAUHP4LBWXFCPDVDEU3BFDSMZF/action/replication_record"}},"created_at":"2026-05-18T03:14:09.440839+00:00","updated_at":"2026-05-18T03:14:09.440839+00:00"}