{"paper":{"title":"Bounds for the Graham-Pollak Theorem for Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anand Babu, Sundar Vishwanathan","submitted_at":"2017-12-18T13:56:30Z","abstract_excerpt":"Let $f_r(n)$ represent the minimum number of complete $r$-partite $r$-graphs required to partition the edge set of the complete $r$-uniform hypergraph on $n$ vertices. The Graham-Pollak theorem states that $f_2(n)=n-1$. An upper bound of $(1+o(1)){n \\choose \\lfloor{\\frac{r}{2}}\\rfloor}$ was known. Recently this was improved to $\\frac{14}{15}(1+o(1)){n \\choose \\lfloor{\\frac{r}{2}}\\rfloor}$ for even $r \\geq 4$. A bound of $\\bigg[\\frac{r}{2}(\\frac{14}{15})^{\\frac{r}{4}}+o(1)\\bigg](1+o(1)){n \\choose \\lfloor{\\frac{r}{2}}\\rfloor}$ was also proved recently. The smallest odd $r$ for which $c_r < 1$ th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06403","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"}