{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:UQTOT6UC4WIMZ7QHIX4XESZHSE","short_pith_number":"pith:UQTOT6UC","schema_version":"1.0","canonical_sha256":"a426e9fa82e590ccfe0745f9724b279119760925d9a55e37a8dbb27bcfb11e0a","source":{"kind":"arxiv","id":"2509.01428","version":2},"attestation_state":"computed","paper":{"title":"Large induced subgraphs with prescribed degree parity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anders Yeo, Gregory Gutin, Jiangdong Ai, Qiwen Guo, Yiming Hao","submitted_at":"2025-09-01T12:36:14Z","abstract_excerpt":"A long-standing conjecture of Caro (Discrete Math, 1994), confirmed by Ferber and Krivelevich (Adv Math, 2022), states that every $n$-vertex graph $G$ without isolated vertices contains an induced subgraph of order linear in $n$ in which every vertex has odd degree. We generalize this result to graphs $G$ whose vertices are labeled by $\\ell: V(G)\\to \\{0,1\\}$. We require, in an induced subgraph, all $0$-labeled vertices to have even degree and all $1$-labeled vertices to have odd degree. Let $h_{\\ell}(G)$ denote the maximum order of such a subgraph. Let $f_{oe}(G)=\\min_{\\ell} h_{\\ell}(G)$ be th"},"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":"2509.01428","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-09-01T12:36:14Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"e17db201fba33c1dd20f8c8e84dd9ea5b01e2117454d9e0bc79038281a4df8eb","abstract_canon_sha256":"3a388fe78d481b4d2e3af848427be4841a7b06ebb9e8d64c043e8be5d7e8f767"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:09:16.470541Z","signature_b64":"B25kiQq/7eQjXDwNnbJoFe5B0sQR1MPWoBlkK7u0n1RaKnM6JdHdHNNbeSYZMDyyvPUXfS5sG8sS3u/L9cIpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a426e9fa82e590ccfe0745f9724b279119760925d9a55e37a8dbb27bcfb11e0a","last_reissued_at":"2026-06-11T01:09:16.469725Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:09:16.469725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large induced subgraphs with prescribed degree parity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anders Yeo, Gregory Gutin, Jiangdong Ai, Qiwen Guo, Yiming Hao","submitted_at":"2025-09-01T12:36:14Z","abstract_excerpt":"A long-standing conjecture of Caro (Discrete Math, 1994), confirmed by Ferber and Krivelevich (Adv Math, 2022), states that every $n$-vertex graph $G$ without isolated vertices contains an induced subgraph of order linear in $n$ in which every vertex has odd degree. We generalize this result to graphs $G$ whose vertices are labeled by $\\ell: V(G)\\to \\{0,1\\}$. We require, in an induced subgraph, all $0$-labeled vertices to have even degree and all $1$-labeled vertices to have odd degree. Let $h_{\\ell}(G)$ denote the maximum order of such a subgraph. Let $f_{oe}(G)=\\min_{\\ell} h_{\\ell}(G)$ be th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01428","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.01428/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":"2509.01428","created_at":"2026-06-11T01:09:16.469863+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.01428v2","created_at":"2026-06-11T01:09:16.469863+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.01428","created_at":"2026-06-11T01:09:16.469863+00:00"},{"alias_kind":"pith_short_12","alias_value":"UQTOT6UC4WIM","created_at":"2026-06-11T01:09:16.469863+00:00"},{"alias_kind":"pith_short_16","alias_value":"UQTOT6UC4WIMZ7QH","created_at":"2026-06-11T01:09:16.469863+00:00"},{"alias_kind":"pith_short_8","alias_value":"UQTOT6UC","created_at":"2026-06-11T01:09:16.469863+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/UQTOT6UC4WIMZ7QHIX4XESZHSE","json":"https://pith.science/pith/UQTOT6UC4WIMZ7QHIX4XESZHSE.json","graph_json":"https://pith.science/api/pith-number/UQTOT6UC4WIMZ7QHIX4XESZHSE/graph.json","events_json":"https://pith.science/api/pith-number/UQTOT6UC4WIMZ7QHIX4XESZHSE/events.json","paper":"https://pith.science/paper/UQTOT6UC"},"agent_actions":{"view_html":"https://pith.science/pith/UQTOT6UC4WIMZ7QHIX4XESZHSE","download_json":"https://pith.science/pith/UQTOT6UC4WIMZ7QHIX4XESZHSE.json","view_paper":"https://pith.science/paper/UQTOT6UC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.01428&json=true","fetch_graph":"https://pith.science/api/pith-number/UQTOT6UC4WIMZ7QHIX4XESZHSE/graph.json","fetch_events":"https://pith.science/api/pith-number/UQTOT6UC4WIMZ7QHIX4XESZHSE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UQTOT6UC4WIMZ7QHIX4XESZHSE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UQTOT6UC4WIMZ7QHIX4XESZHSE/action/storage_attestation","attest_author":"https://pith.science/pith/UQTOT6UC4WIMZ7QHIX4XESZHSE/action/author_attestation","sign_citation":"https://pith.science/pith/UQTOT6UC4WIMZ7QHIX4XESZHSE/action/citation_signature","submit_replication":"https://pith.science/pith/UQTOT6UC4WIMZ7QHIX4XESZHSE/action/replication_record"}},"created_at":"2026-06-11T01:09:16.469863+00:00","updated_at":"2026-06-11T01:09:16.469863+00:00"}