{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:23XYCYULXDUWNFCHIXGMLYQPGP","short_pith_number":"pith:23XYCYUL","schema_version":"1.0","canonical_sha256":"d6ef81628bb8e966944745ccc5e20f33e8c7afc8333841487fd32696bb87a86b","source":{"kind":"arxiv","id":"1908.00665","version":1},"attestation_state":"computed","paper":{"title":"Erdos-Gallai Stability Theorem for Linear Forests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ming-Zhu Chen, Xiao-Dong Zhang","submitted_at":"2019-08-02T00:20:51Z","abstract_excerpt":"The Erd\\H{o}s-Gallai Theorem states that every graph of average degree more than $l-2$ contains a path of order $l$ for $l\\ge 2$. In this paper, we obtain a stability version of the Erd\\H{o}s-Gallai Theorem in terms of minimum degree. Let $G$ be a connected graph of order $n$ and $F=(\\bigcup_{i=1}^kP_{2a_i})\\bigcup(\\bigcup_{i=1}^lP_{2b_i+1})$ be $k+l$ disjoint paths of order $2a_1, \\ldots, 2a_{k}, 2b_1+1, \\ldots, 2b_l+1,$ respectively, where $k\\ge 0$, $0\\le l\\le 2$, and $k+l\\geq 2$. If the minimum degree $\\delta(G)\\ge \\sum_{i=1}^ka_i+\\sum_{i=1}^lb_i-1$, then $F\\subseteq G$ except several class"},"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":"1908.00665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-02T00:20:51Z","cross_cats_sorted":[],"title_canon_sha256":"9aeb6ef7a4eaff57f6d147db36ff80d041e58bac24dc2645786a10cc166e89ea","abstract_canon_sha256":"490a0169b94a0846ab0039438adcacab5627f3fdc160b635339e5e13b16f7f0c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:51:08.008462Z","signature_b64":"ZCPFf3NvDGs8spO7/GPX5CcfX5egFB+aZColkEM0YNjD8c2AoVurLBbiaq+Yse8UlBck56fahWmjUMH5UxQvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6ef81628bb8e966944745ccc5e20f33e8c7afc8333841487fd32696bb87a86b","last_reissued_at":"2026-07-04T23:51:08.007969Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:51:08.007969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Erdos-Gallai Stability Theorem for Linear Forests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ming-Zhu Chen, Xiao-Dong Zhang","submitted_at":"2019-08-02T00:20:51Z","abstract_excerpt":"The Erd\\H{o}s-Gallai Theorem states that every graph of average degree more than $l-2$ contains a path of order $l$ for $l\\ge 2$. In this paper, we obtain a stability version of the Erd\\H{o}s-Gallai Theorem in terms of minimum degree. Let $G$ be a connected graph of order $n$ and $F=(\\bigcup_{i=1}^kP_{2a_i})\\bigcup(\\bigcup_{i=1}^lP_{2b_i+1})$ be $k+l$ disjoint paths of order $2a_1, \\ldots, 2a_{k}, 2b_1+1, \\ldots, 2b_l+1,$ respectively, where $k\\ge 0$, $0\\le l\\le 2$, and $k+l\\geq 2$. If the minimum degree $\\delta(G)\\ge \\sum_{i=1}^ka_i+\\sum_{i=1}^lb_i-1$, then $F\\subseteq G$ except several class"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00665","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/1908.00665/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":"1908.00665","created_at":"2026-07-04T23:51:08.008021+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.00665v1","created_at":"2026-07-04T23:51:08.008021+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00665","created_at":"2026-07-04T23:51:08.008021+00:00"},{"alias_kind":"pith_short_12","alias_value":"23XYCYULXDUW","created_at":"2026-07-04T23:51:08.008021+00:00"},{"alias_kind":"pith_short_16","alias_value":"23XYCYULXDUWNFCH","created_at":"2026-07-04T23:51:08.008021+00:00"},{"alias_kind":"pith_short_8","alias_value":"23XYCYUL","created_at":"2026-07-04T23:51:08.008021+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/23XYCYULXDUWNFCHIXGMLYQPGP","json":"https://pith.science/pith/23XYCYULXDUWNFCHIXGMLYQPGP.json","graph_json":"https://pith.science/api/pith-number/23XYCYULXDUWNFCHIXGMLYQPGP/graph.json","events_json":"https://pith.science/api/pith-number/23XYCYULXDUWNFCHIXGMLYQPGP/events.json","paper":"https://pith.science/paper/23XYCYUL"},"agent_actions":{"view_html":"https://pith.science/pith/23XYCYULXDUWNFCHIXGMLYQPGP","download_json":"https://pith.science/pith/23XYCYULXDUWNFCHIXGMLYQPGP.json","view_paper":"https://pith.science/paper/23XYCYUL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.00665&json=true","fetch_graph":"https://pith.science/api/pith-number/23XYCYULXDUWNFCHIXGMLYQPGP/graph.json","fetch_events":"https://pith.science/api/pith-number/23XYCYULXDUWNFCHIXGMLYQPGP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/23XYCYULXDUWNFCHIXGMLYQPGP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/23XYCYULXDUWNFCHIXGMLYQPGP/action/storage_attestation","attest_author":"https://pith.science/pith/23XYCYULXDUWNFCHIXGMLYQPGP/action/author_attestation","sign_citation":"https://pith.science/pith/23XYCYULXDUWNFCHIXGMLYQPGP/action/citation_signature","submit_replication":"https://pith.science/pith/23XYCYULXDUWNFCHIXGMLYQPGP/action/replication_record"}},"created_at":"2026-07-04T23:51:08.008021+00:00","updated_at":"2026-07-04T23:51:08.008021+00:00"}