{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T01:36:10Z","timestamp":1787362570748,"version":"build-2736575974"},"reference-count":19,"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":[[2019,1]]},"abstract":"<jats:p>We consider the existence of patterned Hamilton cycles in randomly colored random graphs. Given a string $\\Pi$ over a set of colors $\\{1,2,\\ldots,r\\}$, we say that a Hamilton cycle is $\\Pi$-colored if the pattern repeats at intervals of length $|\\Pi|$ as we go around the cycle. We prove a hitting time result for the existence of such a cycle. We also prove a hitting time result for the related notion of $\\Pi$-connected.<\/jats:p>","DOI":"10.1137\/17m1149420","type":"journal-article","created":{"date-parts":[[2019,3,19]],"date-time":"2019-03-19T13:05:11Z","timestamp":1553000711000},"page":"528-545","source":"Crossref","is-referenced-by-count":4,"title":["Pattern Colored Hamilton Cycles in Random Graphs"],"prefix":"10.1137","volume":"33","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"}]}],"member":"351","published-online":{"date-parts":[[2019,3,19]]},"reference":[{"key":"atypb1","unstructured":"M. Anastos and J. Briggs, Packing Directed and Hamilton Cycles Online,arXiv:1612.01965.pdf"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20594"},{"key":"atypb3","unstructured":"B. Bollob\u00e1s,\n                      The evolution of sparse graphs\n                      , in Graph Theory and Combinatorics Proceedings, Cambridge Combinatorial Conference in Honour of Paul Erd\u00f6s, 1984, B. Bollob\u00e1s, ed., pp. 335-357."},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548301005004"},{"key":"atypb5","doi-asserted-by":"crossref","first-page":"R19","DOI":"10.37236\/1213","volume":"2","author":"Cooper C.","year":"1995","journal-title":"Electron. J. Combin."},{"key":"atypb6","first-page":"25","author":"Dudek A.","year":"2018","journal-title":"Electronic J. Combin."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/15M1047106"},{"key":"atypb8","first-page":"167","author":"Ferber A.","year":"2016","journal-title":"New York"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(88)90037-5"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20475"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240050107"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"A. Frieze and M. Karo\u0144ski,\n                      Introduction to Random Graphs\n                      , Cambridge University Press, Cambridge, UK, 2015.","DOI":"10.1017\/CBO9781316339831"},{"key":"atypb13","first-page":"19","author":"Frieze A. M.","year":"2012","journal-title":"Electron. J. Combin."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/140998433"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2012.01.014"},{"key":"atypb16","first-page":"19","author":"Heckel A.","year":"2012","journal-title":"Electron. J. Combin."},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.22003"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-012-1243-2"},{"key":"atypb19","first-page":"24","author":"Molloy M.","year":"2017","journal-title":"Electron. J. Combin."}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1149420","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:51:02Z","timestamp":1787320262000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1149420"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/17M1149420"],"URL":"https:\/\/doi.org\/10.1137\/17m1149420","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}