{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:33:04Z","timestamp":1772253184526,"version":"3.50.1"},"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>Let $G$ be a graph in which each vertex initially has weight 1. In each step, the unit weight from a vertex $u$ to a neighbouring vertex $v$ can be moved, provided that the weight on $v$ is at least as large as the weight on $u$. The unit acquisition number of $G$, denoted by $a_u(G)$, is the minimum cardinality of the set of vertices with positive weight at the end of the process (over all acquisition protocols). In this paper, we investigate the Erd\u0151s-R\u00e9nyi random graph process $(\\mathcal{G}(n,m))_{m =0}^{N}$, where $N = {n \\choose 2}$. We show that asymptotically almost surely $a_u(\\mathcal{G}(n,m)) = 1$ right at the time step the random graph process creates a connected graph. Since trivially $a_u(\\mathcal{G}(n,m)) \\ge 2$ if the graphs is disconnected, the result holds in the strongest possible sense.<\/jats:p>","DOI":"10.37236\/9671","type":"journal-article","created":{"date-parts":[[2021,7,29]],"date-time":"2021-07-29T21:17:47Z","timestamp":1627593467000},"source":"Crossref","is-referenced-by-count":0,"title":["The Unit Acquisition Number of Binomial Random Graphs"],"prefix":"10.37236","volume":"28","author":[{"given":"Konstantinos","family":"Georgiou","sequence":"first","affiliation":[]},{"given":"Somnath","family":"Kundu","sequence":"additional","affiliation":[]},{"given":"Pawe\u0142","family":"Pra\u0142at","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2021,7,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,29]],"date-time":"2021-07-29T21:17:48Z","timestamp":1627593468000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i3p34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,30]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/9671","relation":{"has-preprint":[{"id-type":"doi","id":"10.32920\/24231043.v1","asserted-by":"object"},{"id-type":"doi","id":"10.32920\/24231043","asserted-by":"object"}]},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,30]]},"article-number":"P3.34"}}