{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:S55WBZENDRSF5TR72ZHWGHSR4K","short_pith_number":"pith:S55WBZEN","schema_version":"1.0","canonical_sha256":"977b60e48d1c645ece3fd64f631e51e2986ea0813be5a02d8ee1c81de10464c8","source":{"kind":"arxiv","id":"1308.5188","version":2},"attestation_state":"computed","paper":{"title":"On the geometric Ramsey numbers of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Pu Gao","submitted_at":"2013-08-23T17:49:06Z","abstract_excerpt":"In this paper, we obtain upper bounds for the geometric Ramsey numbers of trees. We prove that $R_c(T_n,H_m)=(n-1)(m-1)+1$ if $T_n$ is a caterpillar and $H_m$ is a Hamiltonian outerplanar graph on $m$ vertices. Moreover, if $T_n$ has at most two non-leaf vertices, then $R_g(T_n,H_m)=(n-1)(m-1)+1$. We also prove that $R_c(T_n,H_m)=O(n^2m)$ and $R_g(T_n,H_m)=O(n^3m^2)$ if $T_n$ is an arbitrary tree on $n$ vertices and $H_m$ is an outerplanar triangulation with pathwidth 2. %Further, we prove a uniform polynomial upper bound for the geometric Ramsey numbers of caterpillars and we also give an upp"},"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":"1308.5188","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-23T17:49:06Z","cross_cats_sorted":[],"title_canon_sha256":"530c6b9152f9d9d581910c28ad84bbbce6f4be884b8567a9719ee7a3ed679cc3","abstract_canon_sha256":"e4d6cd456893f78ee47dab14d7bca427469bd8c764213becbf0968336cf1af0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:22.788932Z","signature_b64":"rPKD401qxU1vx/pOZ6TDtSA6HBrpsoynPRN+vnoiot6SrTj/1iKrtYTuC0PWerpGJsm8DRkjfViH+BkmVan9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"977b60e48d1c645ece3fd64f631e51e2986ea0813be5a02d8ee1c81de10464c8","last_reissued_at":"2026-05-18T03:07:22.788489Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:22.788489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the geometric Ramsey numbers of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Pu Gao","submitted_at":"2013-08-23T17:49:06Z","abstract_excerpt":"In this paper, we obtain upper bounds for the geometric Ramsey numbers of trees. We prove that $R_c(T_n,H_m)=(n-1)(m-1)+1$ if $T_n$ is a caterpillar and $H_m$ is a Hamiltonian outerplanar graph on $m$ vertices. Moreover, if $T_n$ has at most two non-leaf vertices, then $R_g(T_n,H_m)=(n-1)(m-1)+1$. We also prove that $R_c(T_n,H_m)=O(n^2m)$ and $R_g(T_n,H_m)=O(n^3m^2)$ if $T_n$ is an arbitrary tree on $n$ vertices and $H_m$ is an outerplanar triangulation with pathwidth 2. %Further, we prove a uniform polynomial upper bound for the geometric Ramsey numbers of caterpillars and we also give an upp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5188","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":""},"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":"1308.5188","created_at":"2026-05-18T03:07:22.788550+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.5188v2","created_at":"2026-05-18T03:07:22.788550+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5188","created_at":"2026-05-18T03:07:22.788550+00:00"},{"alias_kind":"pith_short_12","alias_value":"S55WBZENDRSF","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"S55WBZENDRSF5TR7","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"S55WBZEN","created_at":"2026-05-18T12:27:59.945178+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/S55WBZENDRSF5TR72ZHWGHSR4K","json":"https://pith.science/pith/S55WBZENDRSF5TR72ZHWGHSR4K.json","graph_json":"https://pith.science/api/pith-number/S55WBZENDRSF5TR72ZHWGHSR4K/graph.json","events_json":"https://pith.science/api/pith-number/S55WBZENDRSF5TR72ZHWGHSR4K/events.json","paper":"https://pith.science/paper/S55WBZEN"},"agent_actions":{"view_html":"https://pith.science/pith/S55WBZENDRSF5TR72ZHWGHSR4K","download_json":"https://pith.science/pith/S55WBZENDRSF5TR72ZHWGHSR4K.json","view_paper":"https://pith.science/paper/S55WBZEN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.5188&json=true","fetch_graph":"https://pith.science/api/pith-number/S55WBZENDRSF5TR72ZHWGHSR4K/graph.json","fetch_events":"https://pith.science/api/pith-number/S55WBZENDRSF5TR72ZHWGHSR4K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S55WBZENDRSF5TR72ZHWGHSR4K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S55WBZENDRSF5TR72ZHWGHSR4K/action/storage_attestation","attest_author":"https://pith.science/pith/S55WBZENDRSF5TR72ZHWGHSR4K/action/author_attestation","sign_citation":"https://pith.science/pith/S55WBZENDRSF5TR72ZHWGHSR4K/action/citation_signature","submit_replication":"https://pith.science/pith/S55WBZENDRSF5TR72ZHWGHSR4K/action/replication_record"}},"created_at":"2026-05-18T03:07:22.788550+00:00","updated_at":"2026-05-18T03:07:22.788550+00:00"}