{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:08:18Z","timestamp":1758823698799},"reference-count":4,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":10443,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1978,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The <jats:italic>n<\/jats:italic>\u2010octahedron <jats:italic>O<\/jats:italic><jats:sub>n<\/jats:sub>, also denoted <jats:italic>K<\/jats:italic>(2,2, \u2026, 2) or <jats:italic>K<\/jats:italic><jats:sub>n(2)<\/jats:sub>, is the complete <jats:italic>n<\/jats:italic>\u2010partite graph with two vertices in each partite set. The formula<jats:disp-formula>\n\n<\/jats:disp-formula>for the (orientable) genus of <jats:italic>O<\/jats:italic><jats:sub>n<\/jats:sub> is conjectured for all <jats:italic>n<\/jats:italic> and proved for <jats:italic>n<\/jats:italic> \u2260 (mof 3). Triangular embeddigns are possible precisely when <jats:italic>n<\/jats:italic> \u2260 2 (mod 3), and the formula is established by exhibiting such embeddings.<\/jats:p>","DOI":"10.1002\/jgt.3190020109","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T06:07:58Z","timestamp":1180418878000},"page":"69-75","source":"Crossref","is-referenced-by-count":10,"title":["The genus of the <i>n<\/i>\u2010octahedron: Regular cases"],"prefix":"10.1002","volume":"2","author":[{"given":"Mark","family":"Jungerman","sequence":"first","affiliation":[]},{"given":"Gerhard","family":"Ringel","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"S. R.Alpert Current maps and non\u2010orientable graph imbeddings. To appear."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1973-13270-7"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65759-7"},{"key":"e_1_2_1_5_2","article-title":"Proof of the Heawood conjecture for non\u2010orientable surfaces","volume":"4467","author":"Youngs J. W. T.","year":"1970","journal-title":"Rand Publication"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190020109","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190020109","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T10:53:47Z","timestamp":1697712827000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190020109"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,3]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1978,3]]}},"alternative-id":["10.1002\/jgt.3190020109"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190020109","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,3]]}}}