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Let $r(S(n,m))$ denote the Ramsey number of the double star $S(n,m)$.\n  In 1979 Grossman, Harary and Klawe have shown that $$r(S(n,m)) = \\max\\{n+2m+2,2n+2\\}$$ for $3 \\leq m \\leq n\\leq \\sqrt{2}m$ and $3m \\leq n$. They conjectured that equality holds for all $m,n \\geq 3$. Using a flag algebra computation, we extend their result showing that $r(S(n,m))\\leq n+ 2m + 2$ for $m \\leq n \\leq 1.699m$. On the other hand, we show that the conjecture fails for $\\fra"},"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":"1605.03612","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-11T20:30:21Z","cross_cats_sorted":[],"title_canon_sha256":"ce8f7339da29d3d81e30c93f5d1bce8eef5b2fdbe311bd1eb3708b09007089f7","abstract_canon_sha256":"f791b801e3d02804ee1c7c55b7d95d719c8abd6bc5f1614b35b1656c51917da8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:00.794110Z","signature_b64":"lbrLM4gUnaqS/66sQSfWUTbcswgNoGDaC3G9PuJ1NH9pZqUXKOJJaDqzhe+MPKPrjpijboWvvYcfhPAM0HU3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1be7c53adf16680e82d40572632cce8ada9f4be53ac763da99b26af754d68b9e","last_reissued_at":"2026-05-18T01:15:00.793727Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:00.793727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of Ramsey numbers of double stars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sergey Norin, Yi Zhao, Yue Ru Sun","submitted_at":"2016-05-11T20:30:21Z","abstract_excerpt":"A double star $S(n,m)$ is the graph obtained by joining the center of a star with $n$ leaves to a center of a star with $m$ leaves by an edge. Let $r(S(n,m))$ denote the Ramsey number of the double star $S(n,m)$.\n  In 1979 Grossman, Harary and Klawe have shown that $$r(S(n,m)) = \\max\\{n+2m+2,2n+2\\}$$ for $3 \\leq m \\leq n\\leq \\sqrt{2}m$ and $3m \\leq n$. They conjectured that equality holds for all $m,n \\geq 3$. Using a flag algebra computation, we extend their result showing that $r(S(n,m))\\leq n+ 2m + 2$ for $m \\leq n \\leq 1.699m$. On the other hand, we show that the conjecture fails for $\\fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03612","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":""},"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":"1605.03612","created_at":"2026-05-18T01:15:00.793775+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.03612v1","created_at":"2026-05-18T01:15:00.793775+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03612","created_at":"2026-05-18T01:15:00.793775+00:00"},{"alias_kind":"pith_short_12","alias_value":"DPT4KOW7CZUA","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"DPT4KOW7CZUA5AWU","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"DPT4KOW7","created_at":"2026-05-18T12:30:12.583610+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/DPT4KOW7CZUA5AWUAVZGGLGORL","json":"https://pith.science/pith/DPT4KOW7CZUA5AWUAVZGGLGORL.json","graph_json":"https://pith.science/api/pith-number/DPT4KOW7CZUA5AWUAVZGGLGORL/graph.json","events_json":"https://pith.science/api/pith-number/DPT4KOW7CZUA5AWUAVZGGLGORL/events.json","paper":"https://pith.science/paper/DPT4KOW7"},"agent_actions":{"view_html":"https://pith.science/pith/DPT4KOW7CZUA5AWUAVZGGLGORL","download_json":"https://pith.science/pith/DPT4KOW7CZUA5AWUAVZGGLGORL.json","view_paper":"https://pith.science/paper/DPT4KOW7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.03612&json=true","fetch_graph":"https://pith.science/api/pith-number/DPT4KOW7CZUA5AWUAVZGGLGORL/graph.json","fetch_events":"https://pith.science/api/pith-number/DPT4KOW7CZUA5AWUAVZGGLGORL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DPT4KOW7CZUA5AWUAVZGGLGORL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DPT4KOW7CZUA5AWUAVZGGLGORL/action/storage_attestation","attest_author":"https://pith.science/pith/DPT4KOW7CZUA5AWUAVZGGLGORL/action/author_attestation","sign_citation":"https://pith.science/pith/DPT4KOW7CZUA5AWUAVZGGLGORL/action/citation_signature","submit_replication":"https://pith.science/pith/DPT4KOW7CZUA5AWUAVZGGLGORL/action/replication_record"}},"created_at":"2026-05-18T01:15:00.793775+00:00","updated_at":"2026-05-18T01:15:00.793775+00:00"}