{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:38:02Z","timestamp":1787326682500,"version":"build-2736575974"},"reference-count":13,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS1661063"],"award-info":[{"award-number":["DMS1661063"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>We study the component structure of the random graph $G=G_{n,m,d}$. Here $d=O(1)$ and $G$ is sampled uniformly from ${\\mathcal G}_{n,m,d}$, the set of graphs with vertex set $[n]$, $m$ edges, and maximum degree at most $d$. If $m=\\mu n\/2$, then we establish a threshold value $\\mu_\\star$ such that if $\\mu&lt;\\mu_\\star$, then with high probability (w.h.p.) the maximum component size is $O(\\log n)$. If $\\mu&gt;\\mu_\\star$, then w.h.p. there is a unique giant component of order $n$ and the remaining components have size $O( \\log n)$.<\/jats:p>","DOI":"10.1137\/19m1249928","type":"journal-article","created":{"date-parts":[[2020,1,2]],"date-time":"2020-01-02T15:14:41Z","timestamp":1577978081000},"page":"53-61","source":"Crossref","is-referenced-by-count":0,"title":["Random Graphs with a Fixed Maximum Degree"],"prefix":"10.1137","volume":"34","author":[{"given":"Alan M.","family":"Frieze","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tomasz","family":"Tkocz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,1,2]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1214\/009117904000000414"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2418(199803)12:2<111::AID-RSA1>3.0.CO;2-#"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(80)80030-8"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01362702"},{"key":"atypb5","unstructured":"R. Durrett,\n                      Probability: Theory and Examples\n                      , 4th ed., Camb. Ser. Stat. Probab. Math. 31, Cambridge University Press, Cambridge, UK, 2010."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20482"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"A. M. Frieze and M. Karo\u0144ski,\n                      Introduction to Random Graphs\n                      , Cambridge University Press, Cambridge, UK, 2016.","DOI":"10.1017\/CBO9781316339831"},{"key":"atypb8","first-page":"9","author":"Gu\u00e9don O.","year":"2014","journal-title":"Warsaw"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20394"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240060204"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548398003526"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20277"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/s11117-011-0130-z"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1249928","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:34:42Z","timestamp":1787322882000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1249928"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1137\/19M1249928"],"URL":"https:\/\/doi.org\/10.1137\/19m1249928","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1]]}}}