{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:45:01Z","timestamp":1759063501028,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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 $f_r(n) \\leq c_r (1+o(1))\\binom{n}{\\lfloor r\/2 \\rfloor}$.It was known that $c_r &lt; 1$ for each even $r \\geq 4$, but this was not known for any odd value of $r$. In this short note, we prove that $c_{295}&lt;1$. Our method also shows that $c_r \\rightarrow 0$, answering another open problem.<\/jats:p>","DOI":"10.37236\/7206","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:41:46Z","timestamp":1578670906000},"source":"Crossref","is-referenced-by-count":3,"title":["Improved Bounds for the Graham-Pollak Problem for Hypergraphs"],"prefix":"10.37236","volume":"25","author":[{"given":"Imre","family":"Leader","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5739-3242","authenticated-orcid":false,"given":"Ta Sheng","family":"Tan","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,1,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:41:16Z","timestamp":1579236076000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/7206","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,1,12]]},"article-number":"P1.4"}}