{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:AYKJSJAYRVQKIVMY7RQQCXN5IM","short_pith_number":"pith:AYKJSJAY","schema_version":"1.0","canonical_sha256":"06149924188d60a45598fc61015dbd433f1b84856e39d89ebdf72bcdd84def4b","source":{"kind":"arxiv","id":"2505.15149","version":1},"attestation_state":"computed","paper":{"title":"Induced subgraphs of graphs with large deficiency","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jin Sun, Xinmin Hou","submitted_at":"2025-05-21T06:07:36Z","abstract_excerpt":"The deficiency of a graph $G$, denoted by $\\kd(G)$, is the number of vertices not saturated by a maximum matching. A bone $B_i$ is the tree obtained by attaching two pendent edges to each of the end vertices of a path $P_{i}$. The local independence number of $G$, denoted by $\\alpha_l(G)$, is defines as the maximum integer $t$ such that $G$ contains an induced star $K_{1,t}$. Motivated by the seminal works of Scott and Seymour~(2016), Chudnovsky et al. (2017, 2020) on finding special types of holes in graphs with large chromatic number and bounded clique number, we establish an analog result b"},"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":"2505.15149","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-21T06:07:36Z","cross_cats_sorted":[],"title_canon_sha256":"71b12c3bee63e4cabc7d24098c3a4913415533417b7727695adfdb638bbf5564","abstract_canon_sha256":"e6a64c24b66a1fb7f555654360d495f45e2555e34a7a3d762358937645b7706b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:06:41.256490Z","signature_b64":"wkeOGsgwRhsk1Gj1HaPJZ8eXPjyM//EUMfJRe8QzvDpP/fPfKAQ9+j1G2tSrxr/m8LneHcyKHHOcb0x0iP/GDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06149924188d60a45598fc61015dbd433f1b84856e39d89ebdf72bcdd84def4b","last_reissued_at":"2026-07-05T11:06:41.256008Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:06:41.256008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Induced subgraphs of graphs with large deficiency","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jin Sun, Xinmin Hou","submitted_at":"2025-05-21T06:07:36Z","abstract_excerpt":"The deficiency of a graph $G$, denoted by $\\kd(G)$, is the number of vertices not saturated by a maximum matching. A bone $B_i$ is the tree obtained by attaching two pendent edges to each of the end vertices of a path $P_{i}$. The local independence number of $G$, denoted by $\\alpha_l(G)$, is defines as the maximum integer $t$ such that $G$ contains an induced star $K_{1,t}$. Motivated by the seminal works of Scott and Seymour~(2016), Chudnovsky et al. (2017, 2020) on finding special types of holes in graphs with large chromatic number and bounded clique number, we establish an analog result b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.15149","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/2505.15149/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":"2505.15149","created_at":"2026-07-05T11:06:41.256065+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.15149v1","created_at":"2026-07-05T11:06:41.256065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.15149","created_at":"2026-07-05T11:06:41.256065+00:00"},{"alias_kind":"pith_short_12","alias_value":"AYKJSJAYRVQK","created_at":"2026-07-05T11:06:41.256065+00:00"},{"alias_kind":"pith_short_16","alias_value":"AYKJSJAYRVQKIVMY","created_at":"2026-07-05T11:06:41.256065+00:00"},{"alias_kind":"pith_short_8","alias_value":"AYKJSJAY","created_at":"2026-07-05T11:06:41.256065+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/AYKJSJAYRVQKIVMY7RQQCXN5IM","json":"https://pith.science/pith/AYKJSJAYRVQKIVMY7RQQCXN5IM.json","graph_json":"https://pith.science/api/pith-number/AYKJSJAYRVQKIVMY7RQQCXN5IM/graph.json","events_json":"https://pith.science/api/pith-number/AYKJSJAYRVQKIVMY7RQQCXN5IM/events.json","paper":"https://pith.science/paper/AYKJSJAY"},"agent_actions":{"view_html":"https://pith.science/pith/AYKJSJAYRVQKIVMY7RQQCXN5IM","download_json":"https://pith.science/pith/AYKJSJAYRVQKIVMY7RQQCXN5IM.json","view_paper":"https://pith.science/paper/AYKJSJAY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.15149&json=true","fetch_graph":"https://pith.science/api/pith-number/AYKJSJAYRVQKIVMY7RQQCXN5IM/graph.json","fetch_events":"https://pith.science/api/pith-number/AYKJSJAYRVQKIVMY7RQQCXN5IM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AYKJSJAYRVQKIVMY7RQQCXN5IM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AYKJSJAYRVQKIVMY7RQQCXN5IM/action/storage_attestation","attest_author":"https://pith.science/pith/AYKJSJAYRVQKIVMY7RQQCXN5IM/action/author_attestation","sign_citation":"https://pith.science/pith/AYKJSJAYRVQKIVMY7RQQCXN5IM/action/citation_signature","submit_replication":"https://pith.science/pith/AYKJSJAYRVQKIVMY7RQQCXN5IM/action/replication_record"}},"created_at":"2026-07-05T11:06:41.256065+00:00","updated_at":"2026-07-05T11:06:41.256065+00:00"}