{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:37:25Z","timestamp":1787323045232,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100010446","name":"Institute for Basic Science","doi-asserted-by":"publisher","award":["IBS-R029-C1"],"award-info":[{"award-number":["IBS-R029-C1"]}],"id":[{"id":"10.13039\/501100010446","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS1952285"],"award-info":[{"award-number":["DMS1952285"]}],"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":[[2023,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Given an [Formula: see text] vertex graph whose edges have colored from one of [Formula: see text] colors [Formula: see text], we define the Hamilton cycle color profile [Formula: see text] to be the set of vectors [Formula: see text] such that there exists a Hamilton cycle that is the concatenation of [Formula: see text] paths [Formula: see text], where [Formula: see text] contains [Formula: see text] edges of color [Formula: see text]. We study [Formula: see text] when the edges are randomly colored. We discuss the profile close to the threshold for the existence of a Hamilton cycle and the threshold for when [Formula: see text].<\/jats:p>","DOI":"10.1137\/21m1403291","type":"journal-article","created":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T13:50:05Z","timestamp":1674049805000},"page":"51-64","source":"Crossref","is-referenced-by-count":2,"title":["Colorful Hamilton Cycles in Random Graphs"],"prefix":"10.1137","volume":"37","author":[{"given":"Debsoumya","family":"Chakraborti","sequence":"first","affiliation":[{"name":"Discrete Mathematics Group, Institute for Basic Science IBS, Daejeon 34126, South Korea."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8481-5615","authenticated-orcid":true,"given":"Alan M.","family":"Frieze","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mihir","family":"Hasabnis","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,1,20]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1149420"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20594"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20616"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.37236\/9066"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548301005004"},{"key":"ref6","first-page":"455","volume":"8","author":"Erd\u0151s P.","year":"1964","journal-title":"Publ Math. 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