{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T17:27:28Z","timestamp":1787506048570,"version":"build-2736575974"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2007,9,1]],"date-time":"2007-09-01T00:00:00Z","timestamp":1188604800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2007,9]]},"abstract":"<jats:p>\n                    Let\n                    <jats:bold>d<\/jats:bold>\n                    =1\u2264\n                    <jats:italic>d<\/jats:italic>\n                    <jats:sub>1<\/jats:sub>\n                    \u2264\n                    <jats:italic>d<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    \u2264\u00b7\u00b7\u00b7.\u2264\n                    <jats:italic>d<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sub>\n                    be a non-decreasing sequence of\n                    <jats:italic>n<\/jats:italic>\n                    positive integers, whose sum is even. Let\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548306008388_inline1\">\n                      <jats:alt-text>$\\mathbb G_{n,{\\bf d}$<\/jats:alt-text>\n                    <\/jats:inline-graphic>\n                    denote the set of graphs with vertex set [\n                    <jats:italic>n<\/jats:italic>\n                    ]={1,2,.\u00a0.\u00a0..,\n                    <jats:italic>n<\/jats:italic>\n                    } in which the degree of vertex\n                    <jats:italic>i<\/jats:italic>\n                    is\n                    <jats:italic>d<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>i<\/jats:italic>\n                    <\/jats:sub>\n                    . Let\n                    <jats:italic>G<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>n<\/jats:italic>\n                      ,\n                      <jats:bold>d<\/jats:bold>\n                    <\/jats:sub>\n                    be chosen uniformly at random from\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548306008388_inline2\">\n                      <jats:alt-text>$\\mathbb G_{n,{\\bf d}$<\/jats:alt-text>\n                    <\/jats:inline-graphic>\n                    . Let\n                    <jats:italic>d<\/jats:italic>\n                    =(\n                    <jats:italic>d<\/jats:italic>\n                    <jats:sub>1<\/jats:sub>\n                    +\n                    <jats:italic>d<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    +\u00b7\u00b7\u00b7.+\n                    <jats:italic>d<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sub>\n                    )\/\n                    <jats:italic>n<\/jats:italic>\n                    be the average degree. We give a condition on\n                    <jats:bold>d<\/jats:bold>\n                    under which we can show that w.h.p. the chromatic number of\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548306008388_inline2\">\n                      <jats:alt-text>$\\mathbb G_{n,{\\bf d}$<\/jats:alt-text>\n                    <\/jats:inline-graphic>\n                    is \u0398(\n                    <jats:italic>d<\/jats:italic>\n                    \/ln\n                    <jats:italic>d<\/jats:italic>\n                    ). This condition is satisfied by graphs with exponential tails as well those with power law tails.\n                  <\/jats:p>","DOI":"10.1017\/s0963548306008388","type":"journal-article","created":{"date-parts":[[2007,1,23]],"date-time":"2007-01-23T10:56:00Z","timestamp":1169549760000},"page":"733-746","source":"Crossref","is-referenced-by-count":7,"title":["On the Chromatic Number of Random Graphs with a Fixed Degree Sequence"],"prefix":"10.1017","volume":"16","author":[{"given":"ALAN","family":"FRIEZE","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"MICHAEL","family":"KRIVELEVICH","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"CLIFF","family":"SMYTH","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2007,9,1]]},"reference":[{"key":"S0963548306008388_manual_ref-2","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2005.162.1335"},{"key":"S0963548306008388_manual_ref-6","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(80)80030-8"},{"key":"S0963548306008388_manual_ref-17","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1017\/S0963548398003526","article-title":"The size of the largest component of a random graph on a fixed degree sequence","volume":"7","author":"Molloy","year":"1998","journal-title":"Combin. 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