{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T08:23:58Z","timestamp":1751531038139},"reference-count":7,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5086,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1992,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For a graphb <jats:italic>F<\/jats:italic> without isolated vertices, let <jats:italic>M<\/jats:italic>(<jats:italic>F<\/jats:italic>; <jats:italic>n<\/jats:italic>) denote the minimum number of monochromatic copies of <jats:italic>F<\/jats:italic> in any 2\u2010coloring of the edges of <jats:italic>K<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>. Burr and Rosta conjectured that <jats:disp-formula>\n\n<\/jats:disp-formula> when <jats:italic>F<\/jats:italic> has order <jats:italic>t<\/jats:italic>, size <jats:italic>u<\/jats:italic>, and <jats:italic>a<\/jats:italic> automorphisms. Independently, Sidorenko and Thomason have shown that the conjecture is false. We give families of graphs <jats:italic>F<\/jats:italic> of order <jats:italic>t<\/jats:italic>, of size <jats:italic>u<\/jats:italic>, and with <jats:italic>a<\/jats:italic> automorphisms where <jats:disp-formula>\n\n<\/jats:disp-formula>.<\/jats:p><jats:p>We show also that the asymptotic value of <jats:italic>M<\/jats:italic>(<jats:italic>F<\/jats:italic>; <jats:italic>n<\/jats:italic>) is not solely a function of the order, size and number of automorphisms of <jats:italic>F<\/jats:italic>. \u00a9 1929 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190160506","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T19:25:02Z","timestamp":1181244302000},"page":"451-458","source":"Crossref","is-referenced-by-count":3,"title":["The minimum number of subgraphs in a graph and its complement"],"prefix":"10.1002","volume":"16","author":[{"given":"Lane","family":"Clark","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Random Graphs","author":"Bollob\u00e1s B.","year":"1985"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190040403"},{"key":"e_1_2_1_4_2","unstructured":"A.Czerniakiewicz Counting monochromatic paths and stars. Preprint."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2310464"},{"key":"e_1_2_1_6_2","unstructured":"A. F.Sidorenko Extermal problems in graph theory and functional analytic inequilities.Proceedings of the All\u2010Union Seminar on Discrete Mathematics and its Applications Moskov. Gos. Univ. Mekh.\u2010Mat. Fak. (1986)99\u2013105."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01139620"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-39.2.246"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190160506","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190160506","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T09:20:29Z","timestamp":1698052829000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190160506"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,11]]},"references-count":7,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1992,11]]}},"alternative-id":["10.1002\/jgt.3190160506"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190160506","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,11]]}}}