{"paper":{"title":"2-Colored Matchings in a 3-Colored K^{3}_{12}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ago Riet, Daniel Gerbner, Diana Piguet, Dominik Vu, Lindsay Erickson, Neal Bushaw, Peter Csorba, Tamas Terpai","submitted_at":"2012-09-10T15:35:06Z","abstract_excerpt":"Let $K_{n}^{r}$ denote the complete $r$-uniform hypergraph on $n$ vertices. A matching $M$ in a hypergraph is a set of pairwise vertex disjoint edges. Recent Ramsey-type results rely on lemmas about the size of monochromatic matchings. A starting point for this study comes from a well-known result of Alon, Frankl, and Lov\\'asz (1986). Our motivation is to find the smallest $n$ such that every $t$-coloring of $K_{n}^{r}$ contains an $s$-colored matching of size $k$. It has been conjectured that in every coloring of the edges of $K_n^r$ with 3 colors there is a 2-colored matching of size at leas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2033","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"}