{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T10:18:23Z","timestamp":1756894703897},"reference-count":10,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":10259,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1978,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Results giving the exact crossing number of an infinite family of graphs on some surface are very scarce. In this paper we show the following: for <jats:italic>G<\/jats:italic> = <jats:italic>Q<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> \u00d7 <jats:italic>K<\/jats:italic><jats:sub>4.4<\/jats:sub>, cr<jats:sub><jats:italic>y<\/jats:italic>(<jats:italic>G<\/jats:italic>)\u2010<jats:italic>m<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>) = 4<jats:italic>m<\/jats:italic>, for 0 \u2a7d = <jats:italic>m<\/jats:italic> \u2a7d 2<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup>. A generalization is obtained, for certain repeated cartesian products of bipartite graphs. Nonorientable analogs are also developed.<\/jats:p>","DOI":"10.1002\/jgt.3190020302","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T06:15:59Z","timestamp":1180419359000},"page":"181-187","source":"Crossref","is-referenced-by-count":14,"title":["On stable crossing numbers"],"prefix":"10.1002","volume":"2","author":[{"given":"Paul C.","family":"Kainen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arthur T.","family":"White","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Introduction to the Theory of Graphs","author":"Behzad M.","year":"1971"},{"key":"e_1_2_1_3_2","article-title":"The crossing number of Cm X K3","author":"Beineke L. W.","journal-title":"J. Combinatorial Theory B"},{"key":"e_1_2_1_4_2","first-page":"532","article-title":"An infinite family of octahedral crossing numbers","volume":"22","author":"Gross J. L.","year":"1975","journal-title":"Notices Amer. Math. Soc. A"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(69)80084-0"},{"key":"e_1_2_1_6_2","unstructured":"P. E.Himelwright On the genus of Hamiltonian groups. Specialist Thesis Western Michigan University 1972."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(72)90042-1"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2307\/2039036"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(70)80087-4"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/1995503"},{"key":"e_1_2_1_11_2","volume-title":"Graphs, Groups and Surfaces","author":"White A. T.","year":"1973"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190020302","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190020302","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T11:01:10Z","timestamp":1699786870000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190020302"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,9]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1978,9]]}},"alternative-id":["10.1002\/jgt.3190020302"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190020302","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,9]]}}}