{"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 $R_3(G) = R(G, G, G)$. Here, we focus on the much less studied combinations between these two cases.\n  Through "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0554","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"}