{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:45:15Z","timestamp":1787323515224,"version":"build-2736575974"},"reference-count":5,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS1363136"],"award-info":[{"award-number":["DMS1363136"]}],"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":[[2021,1]]},"abstract":"<jats:p>We study the Hamiltonicity of the following model of a random graph. Suppose that we partition $[n]$ into $V_1,V_2,\\ldots,V_k$ and add edge $\\{x,y\\}$ to our graph with probability $p$ if there exists $i$ such that $x,y\\in V_i$. Otherwise, we add the edge with probability $q$. We denote this model by ${\\mathcal G}({\\bf n}, p,q)$ and give tight results for Hamiltonicity, including a critical window analysis, under various conditions.<\/jats:p>","DOI":"10.1137\/19m1296069","type":"journal-article","created":{"date-parts":[[2021,8,19]],"date-time":"2021-08-19T14:43:59Z","timestamp":1629384239000},"page":"1854-1880","source":"Crossref","is-referenced-by-count":2,"title":["Hamiltonicity of Random Graphs in the Stochastic Block Model"],"prefix":"10.1137","volume":"35","author":[{"given":"Michael","family":"Anastos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pu","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,8,19]]},"reference":[{"key":"atypb1","first-page":"1","volume":"18","author":"Abbe E.","year":"2018","journal-title":"J. Mach. Learning Res."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(85)80046-9"},{"key":"atypb3","unstructured":"A. M. Frieze,\n                      Hamilton Cycles in Random Graphs: A Bibliography\n                      , preprint,https:\/\/arxiv.org\/abs\/1901.07139, 2019."},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"A. M. Frieze and M. Karo\u0144ski,\n                      Introduction to Random Graphs\n                      , Cambridge University Press, 2015.","DOI":"10.1017\/CBO9781316339831"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90021-3"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1296069","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:06:59Z","timestamp":1787321219000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1296069"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/19M1296069"],"URL":"https:\/\/doi.org\/10.1137\/19m1296069","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}