{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T20:10:56Z","timestamp":1774555856231,"version":"3.50.1"},"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>In 2013, Bollob\u00e1s, Mitsche, and Pra\u0142at gave upper and lower bounds for the likely metric dimension of random Erd\u0151s-R\u00e9nyi graphs $G(n,p)$ for a large range of expected degrees. However, their results only apply when $d=pn=\\omega(\\log^5 n)$, leaving open sparser random graphs with $d=O(\\log^5 n)$ or $d=o(\\log^5n)$. Here we provide upper and lower bounds on the likely metric dimension of $G(n,p)$ in a range of $d$ starting just above the connectivity transition, i.e., where $d=c \\log n$ for some constant $c &gt; 1$, up to $d=O(\\log^5 n)$. Our lower bound technique is based on an entropic argument which is weaker but more general than the use of Suen's inequality by Bollob\u00e1s, Mitsche, and Pra\u0142at, whereas our upper bound is similar to theirs.<\/jats:p>","DOI":"10.37236\/14094","type":"journal-article","created":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T19:48:30Z","timestamp":1774554510000},"source":"Crossref","is-referenced-by-count":0,"title":["The Metric Dimension of Sparse Random Graphs"],"prefix":"10.37236","volume":"33","author":[{"given":"Josep","family":"D\u00edaz","sequence":"first","affiliation":[]},{"given":"Harrison","family":"Hartle","sequence":"additional","affiliation":[]},{"given":"Cristopher","family":"Moore","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,3,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p59\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p59\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T19:48:30Z","timestamp":1774554510000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/14094","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,27]]},"article-number":"P1.59"}}