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We study the bounds on various 3-color Ramsey numbers $R(G_1, G_2, G_3)$, where $G_i \\in \\{K_3, K_3+e, K_4-e, K_4\\}$. The minimal and maximal combinations of $G_i$'s correspond to the classical Ramsey numbers $R_3(K_3)$ and $R_3(K_4)$, respectively, where $R_3(G) = R(G, G, G)$. Here, we focus on the much less studied combinations between these two cases.\n  Through "},"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":"1201.0554","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-03T00:18:43Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"cb51435f181913d18ff5fd9d9bf969bc6ed466bc5e57443745b4926c2496ebad","abstract_canon_sha256":"1ab077e98ebdd0cf7eac435fb7e195da06502e103e6f8ba761bf4af1e8f512c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:52.167969Z","signature_b64":"ytUd7HvP0aZYp2I2WXwvo2CqheUL9E1mPiYi0pVnFuAt4qCuIyzVBar4IWa4/TdjBGiLu4CGm3Aemz1/vIf4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2269e88b00cce3f0c432b6213fc8bd3bb13fbae7d2cb0bc7de2b4f9110054fc4","last_reissued_at":"2026-05-18T02:50:52.167522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:52.167522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Some Multicolor Ramsey Numbers Involving $K_3+e$ and $K_4-e$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Daniel S. Shetler, Michael A. Wurtz, Stanis{\\l}aw P. Radziszowski","submitted_at":"2012-01-03T00:18:43Z","abstract_excerpt":"The Ramsey number $R(G_1, G_2, G_3)$ is the smallest positive integer $n$ such that for all 3-colorings of the edges of $K_n$ there is a monochromatic $G_1$ in the first color, $G_2$ in the second color, or $G_3$ in the third color. We study the bounds on various 3-color Ramsey numbers $R(G_1, G_2, G_3)$, where $G_i \\in \\{K_3, K_3+e, K_4-e, K_4\\}$. The minimal and maximal combinations of $G_i$'s correspond to the classical Ramsey numbers $R_3(K_3)$ and $R_3(K_4)$, respectively, where $R_3(G) = R(G, G, G)$. 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