{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:37:15Z","timestamp":1787326635439,"version":"build-2736575974"},"reference-count":15,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>Let $\\mathbf{d}=d_1\\leq d_2\\leq\\dots\\leq d_n$ be a nondecreasing sequence of n positive integers whose sum is even. Let $\\mathcal{G}_{n,\\mathbf{d}}$ denote the set of graphs with vertex set $[n]=\\{1,2,\\dots,n\\}$ in which the degree of vertex i is $d_i$. Let $G_{n,\\mathbf{d}}$ be chosen uniformly at random from $\\mathcal{G}_{n,\\mathbf{d}}$. It will be apparent from section 4.3 that all of the sequences we are considering will be graphic. We give a condition on $\\mathbf{d}$ under which we can show that whp $\\mathcal{G}_{n,\\mathbf{d}}$ is Hamiltonian. This condition is satisfied by graphs with exponential tails as well those with power law tails.<\/jats:p>","DOI":"10.1137\/080741379","type":"journal-article","created":{"date-parts":[[2010,5,21]],"date-time":"2010-05-21T18:10:20Z","timestamp":1274465420000},"page":"558-569","source":"Crossref","is-referenced-by-count":3,"title":["Hamilton Cycles in Random Graphs with a Fixed Degree Sequence"],"prefix":"10.1137","volume":"24","author":[{"given":"Colin","family":"Cooper","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Krivelevich","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,5,21]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.2001.10504428"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(78)90059-6"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(80)80030-8"},{"key":"R4","unstructured":"B. Bollob\u00e1s,\n                      Random Graphs\n                      , 2nd ed., Cambridge Stud. Adv. Math. 73, Cambridge University Press, Cambridge, UK, 2001."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20040"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1017\/S096354830400611X"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548306008388"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"A. M. Frieze and B. G. Pittel,\n                      Perfect matchings in random graphs with prescribed minimal degree\n                      , in Trends Math., Birkh\u00e4user, Basel, 2004, pp. 95\u2013132.","DOI":"10.1007\/978-3-0348-7915-6_11"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01275671"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(13)80042-X"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(90)90029-E"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240060204"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548398003526"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(76)90068-6"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"N. C. Wormald,\n                      Models of random regular graphs\n                      , in Surveys in Combinatorics, London Math. Soc. Lecture Note Ser. 267, Cambridge University Press, Cambridge, UK, 1999, pp. 239\u2013298.","DOI":"10.1017\/CBO9780511721335.010"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080741379","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:34:00Z","timestamp":1787322840000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080741379"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080741379"],"URL":"https:\/\/doi.org\/10.1137\/080741379","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}