{"paper":{"title":"Improved Bounds for the Graham-Pollak Problem for Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Imre Leader, Ta Sheng Tan","submitted_at":"2017-08-06T14:49:00Z","abstract_excerpt":"For a fixed $r$, let $f_r(n)$ denote the minimum number of complete $r$-partite $r$-graphs needed to partition the complete $r$-graph on $n$ vertices. The Graham-Pollak theorem asserts that $f_2(n)=n-1$. An easy construction shows that $f_r(n) \\leq (1+o(1))\\binom{n}{\\lfloor r/2 \\rfloor}$, and we write $c_r$ for the least number such that $f_r(n) \\leq c_r (1+o(1))\\binom{n}{\\lfloor r/2 \\rfloor}$.\n  It was known that $c_r < 1$ for each even $r \\geq 4$, but this was not known for any odd value of $r$. In this short note, we prove that $c_{295}<1$. Our method also shows that $c_r \\rightarrow 0$, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01898","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"}