{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:M3QTXNUEUJ56R2UYYOGNC63C35","short_pith_number":"pith:M3QTXNUE","schema_version":"1.0","canonical_sha256":"66e13bb684a27be8ea98c38cd17b62df694d3415c971e1e4b6da810e7259e51f","source":{"kind":"arxiv","id":"1309.1312","version":1},"attestation_state":"computed","paper":{"title":"Excluding induced subdivisions of the bull and related graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Scott, Irena Penev, Maria Chudnovsky, Nicolas Trotignon","submitted_at":"2013-09-05T11:18:30Z","abstract_excerpt":"For any graph $H$, let ${\\rm Forb}^*(H)$ be the class of graphs with no induced subdivision of $H$. It was conjectured in [A.D. Scott, Induced trees in graphs of large chromatic number, {\\em Journal of Graph Theory}, 24:297--311, 1997] that, for every graph $H$, there is a function $f_H:\\mathbb{N} \\rightarrow \\mathbb{R}$ such that for every graph $G \\in {\\rm Forb}^*(H)$, $\\chi(G) \\leq f_H(\\omega(G))$. We prove this conjecture for several graphs $H$, namely the paw (a triangle with a pendant edge), the bull (a triangle with two vertex-disjoint pendant edges), and what we call a \"necklace,\" that"},"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":"1309.1312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-05T11:18:30Z","cross_cats_sorted":[],"title_canon_sha256":"fdba563bb96a921e5cb67679b55bf3e933129d35677ffa61c8d33552db524119","abstract_canon_sha256":"550967de0898fb3ab9498e6de6bac784fb7a7f8b2dd3d8a72e8f57f30beeb1f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:07.630075Z","signature_b64":"EVYGx0sxqtYMy93rVzfmeNzmGIONtIZRbKy4k6eYNFGT4IFzQ6P7mD+lL3z/ybAEoddcHmbhEQrRSvBZCCo1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66e13bb684a27be8ea98c38cd17b62df694d3415c971e1e4b6da810e7259e51f","last_reissued_at":"2026-05-18T03:14:07.629471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:07.629471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Excluding induced subdivisions of the bull and related graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Scott, Irena Penev, Maria Chudnovsky, Nicolas Trotignon","submitted_at":"2013-09-05T11:18:30Z","abstract_excerpt":"For any graph $H$, let ${\\rm Forb}^*(H)$ be the class of graphs with no induced subdivision of $H$. It was conjectured in [A.D. Scott, Induced trees in graphs of large chromatic number, {\\em Journal of Graph Theory}, 24:297--311, 1997] that, for every graph $H$, there is a function $f_H:\\mathbb{N} \\rightarrow \\mathbb{R}$ such that for every graph $G \\in {\\rm Forb}^*(H)$, $\\chi(G) \\leq f_H(\\omega(G))$. We prove this conjecture for several graphs $H$, namely the paw (a triangle with a pendant edge), the bull (a triangle with two vertex-disjoint pendant edges), and what we call a \"necklace,\" that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1312","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":"1309.1312","created_at":"2026-05-18T03:14:07.629556+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.1312v1","created_at":"2026-05-18T03:14:07.629556+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1312","created_at":"2026-05-18T03:14:07.629556+00:00"},{"alias_kind":"pith_short_12","alias_value":"M3QTXNUEUJ56","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"M3QTXNUEUJ56R2UY","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"M3QTXNUE","created_at":"2026-05-18T12:27:51.066281+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/M3QTXNUEUJ56R2UYYOGNC63C35","json":"https://pith.science/pith/M3QTXNUEUJ56R2UYYOGNC63C35.json","graph_json":"https://pith.science/api/pith-number/M3QTXNUEUJ56R2UYYOGNC63C35/graph.json","events_json":"https://pith.science/api/pith-number/M3QTXNUEUJ56R2UYYOGNC63C35/events.json","paper":"https://pith.science/paper/M3QTXNUE"},"agent_actions":{"view_html":"https://pith.science/pith/M3QTXNUEUJ56R2UYYOGNC63C35","download_json":"https://pith.science/pith/M3QTXNUEUJ56R2UYYOGNC63C35.json","view_paper":"https://pith.science/paper/M3QTXNUE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.1312&json=true","fetch_graph":"https://pith.science/api/pith-number/M3QTXNUEUJ56R2UYYOGNC63C35/graph.json","fetch_events":"https://pith.science/api/pith-number/M3QTXNUEUJ56R2UYYOGNC63C35/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M3QTXNUEUJ56R2UYYOGNC63C35/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M3QTXNUEUJ56R2UYYOGNC63C35/action/storage_attestation","attest_author":"https://pith.science/pith/M3QTXNUEUJ56R2UYYOGNC63C35/action/author_attestation","sign_citation":"https://pith.science/pith/M3QTXNUEUJ56R2UYYOGNC63C35/action/citation_signature","submit_replication":"https://pith.science/pith/M3QTXNUEUJ56R2UYYOGNC63C35/action/replication_record"}},"created_at":"2026-05-18T03:14:07.629556+00:00","updated_at":"2026-05-18T03:14:07.629556+00:00"}