{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T21:07:10Z","timestamp":1767992830287,"version":"3.49.0"},"reference-count":11,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5056,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1992,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Rosenfeld (1971) proved that the Total Colouring Conjecture holds for balanced complete <jats:italic>r<\/jats:italic>\u2010partite graphs. Bermond (1974) determined the exact total chromatic number of every balanced complete <jats:italic>r<\/jats:italic>\u2010partite graph. Rosenfeld's result had been generalized recently to complete <jats:italic>r<\/jats:italic>\u2010partite graphs by Yap (1989). The main result of this paper is to prove that the total chromatic number of every complete <jats:italic>r<\/jats:italic>\u2010partite graph <jats:italic>G<\/jats:italic> of odd order is \u0394 (<jats:italic>G<\/jats:italic>) + 1. This result gives a partial generalization of Bermond's theorem.<\/jats:p>","DOI":"10.1002\/jgt.3190160608","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T22:20:22Z","timestamp":1181254822000},"page":"629-634","source":"Crossref","is-referenced-by-count":10,"title":["Total chromatic number of complete <i>r<\/i>\u2010partite graphs"],"prefix":"10.1002","volume":"16","author":[{"given":"K. H.","family":"Chew","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H. P.","family":"Yap","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"M.Behzad Graphs and Their Chromatic Numbers Doctoral thesis Michigan State University (1965)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-42.1.226"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-9.2.279"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771690"},{"key":"e_1_2_1_6_2","first-page":"25","article-title":"On an estimate of the chromatic class of a p\u2010graph [Russian]","volume":"3","author":"Vizing V. G.","year":"1964","journal-title":"Diskret. Analiz"},{"key":"e_1_2_1_7_2","first-page":"117","article-title":"Some unsolved problems in graph theory","volume":"23","author":"Vizing V. G.","year":"1968","journal-title":"Uspehi Mat. Nauk"},{"key":"e_1_2_1_7_3","doi-asserted-by":"publisher","DOI":"10.1070\/RM1968v023n06ABEH001252"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511662065"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/21.2.159"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700033176"},{"key":"e_1_2_1_11_2","unstructured":"H. P.Yap Total chromatic number of graphs of high degree III. Submitted for publication."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190160608","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190160608","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T20:14:56Z","timestamp":1698092096000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190160608"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,12]]},"references-count":11,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1992,12]]}},"alternative-id":["10.1002\/jgt.3190160608"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190160608","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,12]]}}}