{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:46Z","timestamp":1753893826136,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper we introduce the notion of minimum-weight edge-discriminators in hypergraphs, and study their various properties. For a hypergraph $\\mathcal H=(\\mathcal V, \\mathscr E)$, a function $\\lambda: \\mathcal V\\rightarrow \\mathbb Z^{+}\\cup\\{0\\}$ is said to be an edge-discriminator on $\\mathcal H$ if $\\sum_{v\\in E_i}{\\lambda(v)}&gt;0$, for all hyperedges $E_i\\in \\mathscr E$, and $\\sum_{v\\in E_i}{\\lambda(v)}\\ne \\sum_{v\\in E_j}{\\lambda(v)}$, for every two distinct hyperedges $E_i, E_j \\in \\mathscr E$. An optimal edge-discriminator on $\\mathcal H$, to be denoted by $\\lambda_\\mathcal H$, is an edge-discriminator on $\\mathcal H$ satisfying $\\sum_{v\\in \\mathcal V}\\lambda_\\mathcal H (v)=\\min_\\lambda\\sum_{v\\in \\mathcal V}{\\lambda(v)}$, where the minimum is taken over all edge-discriminators on $\\mathcal H$.\u00a0 We prove that any hypergraph $\\mathcal H=(\\mathcal V, \\mathscr E)$,\u00a0 with $|\\mathscr E|=m$, satisfies $\\sum_{v\\in \\mathcal V} \\lambda_\\mathcal H(v)\\leq m(m+1)\/2$, and the equality holds if and only if the elements of $\\mathscr E$ are mutually disjoint. For $r$-uniform hypergraphs $\\mathcal H=(\\mathcal V, \\mathscr E)$, it follows from earlier results on Sidon sequences that $\\sum_{v\\in \\mathcal V}\\lambda_{\\mathcal H}(v)\\leq |\\mathcal V|^{r+1}+o(|\\mathcal V|^{r+1})$, and the bound is attained up to a constant factor by the complete $r$-uniform hypergraph. Finally, we show that no optimal edge-discriminator on any hypergraph $\\mathcal H=(\\mathcal V, \\mathscr E)$, with $|\\mathscr E|=m~(\\geq 3)$, satisfies $\\sum_{v\\in \\mathcal V} \\lambda_\\mathcal H (v)=m(m+1)\/2-1$. This shows that all integer values between $m$ and $m(m+1)\/2$ cannot be the weight of an optimal edge-discriminator of a hypergraph, and this raises many other interesting combinatorial questions.<\/jats:p>","DOI":"10.37236\/3551","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:56:46Z","timestamp":1578704206000},"source":"Crossref","is-referenced-by-count":1,"title":["Minimum-Weight Edge Discriminators in Hypergraphs"],"prefix":"10.37236","volume":"21","author":[{"given":"Bhaswar B.","family":"Bhattacharya","sequence":"first","affiliation":[]},{"given":"Sayantan","family":"Das","sequence":"additional","affiliation":[]},{"given":"Shirshendu","family":"Ganguly","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,8,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i3p18\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i3p18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:49:55Z","timestamp":1579258195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i3p18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8,6]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2014,7,3]]}},"URL":"https:\/\/doi.org\/10.37236\/3551","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,8,6]]},"article-number":"P3.18"}}