{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T02:24:30Z","timestamp":1778034270386,"version":"3.51.4"},"reference-count":14,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4176,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1995,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>James Propp<\/jats:p><jats:p>The most familiar construction of graphs whose clique number is much smaller than their chromatic number is due to Mycielski, who constructed a sequence <jats:italic>G<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> of triangle\u2010free graphs with X(<jats:italic>G<\/jats:italic><jats:sub>n<\/jats:sub>) = <jats:italic>n<\/jats:italic>. In this article, we calculate the fractional chromatic number of <jats:italic>G<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> and show that this sequence of numbers satisfies the unexpected recurrence <jats:italic>a<\/jats:italic><jats:sub>n+1<\/jats:sub> = <jats:italic>a<\/jats:italic><jats:sub>n<\/jats:sub> + (1\/<jats:italic>a<\/jats:italic><jats:sub>n<\/jats:sub>). \u00a9 1995 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190190313","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T13:53:42Z","timestamp":1180187622000},"page":"411-416","source":"Crossref","is-referenced-by-count":57,"title":["The fractional chromatic number of mycielski's graphs"],"prefix":"10.1002","volume":"19","author":[{"given":"Michael","family":"Larsen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James","family":"Propp","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Ullman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.2307\/2323314"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(79)90148-1"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70329-7"},{"key":"e_1_2_1_5_2","article-title":"Fractional colorings with large denominators","author":"Fisher D. C.","journal-title":"J. Graph Theory."},{"key":"e_1_2_1_6_2","first-page":"155","article-title":"Analogues of the Shannon capacity of a graph","volume":"12","author":"Hell P.","year":"1982","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/5.3.302"},{"key":"e_1_2_1_8_2","volume-title":"The Green Book: 100 Problems for Undergraduate Mathematics Competitions","author":"Hardy K.","year":"1985"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(78)90022-5"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1979.1055985"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177693169"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.4064\/cm-3-2-161-162"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8214-0"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/0405011"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1956.1056798"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190190313","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190190313","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T20:58:11Z","timestamp":1698353891000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190190313"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,5]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,5]]}},"alternative-id":["10.1002\/jgt.3190190313"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190190313","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,5]]}}}