{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:21:33Z","timestamp":1759335693502,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Given an $r$-uniform hypergraph $H=(V,E)$ and a weight function $\\omega:E\\to\\{1,\\dots,w\\}$, a coloring of vertices of~$H$, induced by~$\\omega$, is defined by $c(v) = \\sum_{e\\ni v} w(e)$ for all $v\\in V$. If there exists such a coloring that is strong (that means in each edge no color appears more than once), then we say that $H$ is strongly $w$-weighted. Similarly, if the coloring is weak (that means there is no monochromatic edge), then we say that $H$ is weakly $w$-weighted. In this paper, we show that almost all 3 or 4-uniform hypergraphs are strongly 2-weighted (but not 1-weighted) and almost all $5$-uniform hypergraphs are either 1 or 2 strongly weighted (with a nontrivial distribution). Furthermore, for $r\\ge 6$ we show that almost all $r$-uniform hypergraphs are strongly 1-weighted. We complement these results by showing that almost all 3-uniform hypergraphs are weakly 2-weighted but not 1-weighted and for $r\\ge 4$ almost all $r$-uniform hypergraphs are weakly 1-weighted.\u00a0These results extend a previous work of Addario-Berry, Dalal and Reed for graphs. We also prove general lower bounds and show that there are $r$-uniform hypergraphs which are not strongly $(r^2-r)$-weighted and not weakly 2-weighted. Finally, we show that determining whether a particular uniform hypergraph is strongly 2-weighted is NP-complete.<\/jats:p>","DOI":"10.37236\/5709","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:58:05Z","timestamp":1578689885000},"source":"Crossref","is-referenced-by-count":7,"title":["Weak and Strong Versions of the 1-2-3 Conjecture for Uniform Hypergraphs"],"prefix":"10.37236","volume":"23","author":[{"given":"Patrick","family":"Bennett","sequence":"first","affiliation":[]},{"given":"Andrzej","family":"Dudek","sequence":"additional","affiliation":[]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[]},{"given":"Laars","family":"Helenius","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,6,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p46\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p46\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:27:44Z","timestamp":1579238864000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i2p46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,10]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/5709","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,6,10]]},"article-number":"P2.46"}}