{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:P7PFNH7TDTAG5KZ2FE2LXLW2OC","short_pith_number":"pith:P7PFNH7T","schema_version":"1.0","canonical_sha256":"7fde569ff31cc06eab3a2934bbaeda70904c2370644530ed157c2e21d2824de3","source":{"kind":"arxiv","id":"1110.2725","version":4},"attestation_state":"computed","paper":{"title":"Tur\\'an's problem and Ramsey numbers for trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lin-Lin Wang, Yi-Li Wu, Zhi-Hong Sun","submitted_at":"2011-10-12T18:12:56Z","abstract_excerpt":"Let $T_n^1=(V,E_1)$ and $T_n^2=(V,E_2)$ be the trees on $n$ vertices with $V=\\{v_0,v_1,\\ldots,v_{n-1}\\}$, $E_1=\\{v_0v_1,\\ldots,v_0v_{n-3},v_{n-4}v_{n-2},v_{n-3}v_{n-1}\\}$, and $E_2=\\{v_0v_1,\\ldots,$ $v_0v_{n-3},v_{n-3}v_{n-2}, v_{n-3}v_{n-1}\\}$. In this paper, for $p\\ge n\\ge 5$ we obtain explicit formulas for $\\ex(p;T_n^1)$ and $\\ex(p;T_n^2)$, where $\\ex(p;L)$ denotes the maximal number of edges in a graph of order $p$ not containing $L$ as a subgraph. Let $r(G\\sb 1, G\\sb 2)$ be the Ramsey number of the two graphs $G_1$ and $G_2$. In this paper we also obtain some explicit formulas for $r(T_m,"},"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":"1110.2725","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-12T18:12:56Z","cross_cats_sorted":[],"title_canon_sha256":"9a7711a12d5f81bf754ebb9d6871e80049523d8982446b7187af8fb2bce44f2a","abstract_canon_sha256":"5460bfab9065cdb8e0339d2ed22719b8f40ba931ed5546f21dfda260290dd5d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:12.777469Z","signature_b64":"ha99hVlvPDBPDzHiZ+fo3W3NxuxdTfm/fG/uoKngx1oCFDbw6rfFKVu5KoaPxmWPaMIVYeysjF0pW1ibm+d2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fde569ff31cc06eab3a2934bbaeda70904c2370644530ed157c2e21d2824de3","last_reissued_at":"2026-05-18T02:17:12.776861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:12.776861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tur\\'an's problem and Ramsey numbers for trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lin-Lin Wang, Yi-Li Wu, Zhi-Hong Sun","submitted_at":"2011-10-12T18:12:56Z","abstract_excerpt":"Let $T_n^1=(V,E_1)$ and $T_n^2=(V,E_2)$ be the trees on $n$ vertices with $V=\\{v_0,v_1,\\ldots,v_{n-1}\\}$, $E_1=\\{v_0v_1,\\ldots,v_0v_{n-3},v_{n-4}v_{n-2},v_{n-3}v_{n-1}\\}$, and $E_2=\\{v_0v_1,\\ldots,$ $v_0v_{n-3},v_{n-3}v_{n-2}, v_{n-3}v_{n-1}\\}$. In this paper, for $p\\ge n\\ge 5$ we obtain explicit formulas for $\\ex(p;T_n^1)$ and $\\ex(p;T_n^2)$, where $\\ex(p;L)$ denotes the maximal number of edges in a graph of order $p$ not containing $L$ as a subgraph. Let $r(G\\sb 1, G\\sb 2)$ be the Ramsey number of the two graphs $G_1$ and $G_2$. 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