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In this paper, we show that the Ramsey number $$r(G,tB_k)=2n+t-2$$ provided $n\\ge 111t^3k^3$. Our result extends the work of Erd\\H{o}s, Faudree, Rousseau, and Schelp (1988), who established the corresponding result for $G$ being a tree and $t=1$."},"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":"2507.09827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-07-13T23:36:48Z","cross_cats_sorted":[],"title_canon_sha256":"e723d437edfe31d1eee6f6137332e8e80115c4bbff29820aae28a97b748a8673","abstract_canon_sha256":"c37c1b3ca2fa1de6ec281496cf049f503fef9b3efd08c7b518a9d0f4ec4b6ceb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:40.376893Z","signature_b64":"MN4Uhl46QQ9My56pAnRFsWj98m0JFF3WTq8ww3+p75UZ++1yyPnyxa2ZHhY1m3BIockdzI03rKhvbkeGwJHOAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e988e373bc0646347f28107c321c9f0ab5006a72da39d1293468b43c428ce8e","last_reissued_at":"2026-07-05T11:36:40.376342Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:40.376342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ramsey numbers of sparse graphs versus disjoint books","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ting Huang, Yanbo Zhang, Yaojun Chen","submitted_at":"2025-07-13T23:36:48Z","abstract_excerpt":"Let $B_k$ denote a book on $k+2$ vertices and $tB_k$ be $t$ vertex-disjoint $B_k$'s. 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