{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T13:06:34Z","timestamp":1769691994668,"version":"3.49.0"},"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 this paper, we show that the domination number  $D$ of a random graph enjoys as sharp a concentration as does its chromatic number $\\chi$.  We first prove this fact for the sequence of graphs  $\\{G(n,p_n\\},\\; n\\to\\infty$, where a two point concentration is obtained with high probability for $p_n=p$ (fixed) or for a  sequence $p_n$ that approaches zero sufficiently slowly.  We then consider the infinite graph $G({\\bf Z}^+, p)$, where $p$ is fixed,  and prove a three point concentration for the domination  number with probability one. The main results are  proved using the second moment method together with the Borel Cantelli lemma.<\/jats:p>","DOI":"10.37236\/1581","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:06:54Z","timestamp":1578708414000},"source":"Crossref","is-referenced-by-count":29,"title":["On the Domination Number of a Random Graph"],"prefix":"10.37236","volume":"8","author":[{"given":"Ben","family":"Wieland","sequence":"first","affiliation":[]},{"given":"Anant P.","family":"Godbole","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2001,10,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r37\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:16:45Z","timestamp":1579324605000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1r37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,10,11]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1581","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,10,11]]},"article-number":"R37"}}