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In 2022, the third author and others gave lower and upper bounds of the Ramsey number $\\mathrm{R}(W_n,W_n)$, where $W_n$ is the wheel graph with $n$ vertices. In this paper, we improve their bounds by showing that $3n-2\\leq \\mathrm{R}(W_n,W_n)\\leq 6n-6$ for even $n\\geq 8$ and $2n\\leq \\mathrm{R}(W_n,W_n)\\leq \\frac{9n-7}{2}$ for odd $n\\geq 7$. Furthermore, we give recursive bounds for the $k$-colo"},"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":"2605.22116","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T07:48:14Z","cross_cats_sorted":[],"title_canon_sha256":"66f300fd20e34777f94b036bedb7104c1868c383dd7242a51baf893c5946ac19","abstract_canon_sha256":"a3a3d19899095f144ffc016c4401d4d1213cbb996eb755b4f0ca65008eb08eda"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:26.669256Z","signature_b64":"1nO46zW/elL1IcYxG9/k78/J7fWeP/3PIJlBevJ0AH/QZUV5YEtFt0noTWcjnWpg3TIgssHoqQsjqlDsBfydDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b77836ea304d1f6d4632359dad924f55f282e3533fd8d32022f9f3fcd8a9a00","last_reissued_at":"2026-05-22T01:04:26.668530Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:26.668530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diagonal Ramsey numbers for wheels","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maoxuan Li, Masaki Kashima, Yaping Mao","submitted_at":"2026-05-21T07:48:14Z","abstract_excerpt":"The Ramsey number $\\mathrm{R}(G_1,G_2)$ is the smallest integer $N$ such that any red-blue coloring of the edges of the complete graph $K_N$ contains either a red copy of $G_1$ or a blue copy of $G_2$. In 2022, the third author and others gave lower and upper bounds of the Ramsey number $\\mathrm{R}(W_n,W_n)$, where $W_n$ is the wheel graph with $n$ vertices. In this paper, we improve their bounds by showing that $3n-2\\leq \\mathrm{R}(W_n,W_n)\\leq 6n-6$ for even $n\\geq 8$ and $2n\\leq \\mathrm{R}(W_n,W_n)\\leq \\frac{9n-7}{2}$ for odd $n\\geq 7$. 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