{"paper":{"title":"The chromatic spectrum of 3-uniform bi-hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kaishun Wang, Kefeng Diao, Ping Zhao","submitted_at":"2011-05-13T09:48:18Z","abstract_excerpt":"Let $S=\\{n_1,n_2,...,n_t\\}$ be a finite set of positive integers with $\\min(S)\\geq 3$ and $t\\geq 2$. For any positive integers $s_1,s_2,...,s_t$, we construct a family of 3-uniform bi-hypergraphs ${\\cal H}$ with the feasible set $S$ and $r_{n_i}=s_i, i=1,2,...,t$, where each $r_{n_i}$ is the $n_i$th component of the chromatic spectrum of ${\\cal H}$. As a result, we solve one open problem for 3-uniform bi-hypergraphs proposed by Bujt\\'{a}s and Tuza in 2008. Moreover, we find a family of sub-hypergraphs with the same feasible set and the same chromatic spectrum as it's own. In particular, we obt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2672","kind":"arxiv","version":1},"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"}