{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T13:48:36Z","timestamp":1773150516829,"version":"3.50.1"},"reference-count":7,"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":10078,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1979,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>G<\/jats:italic><jats:sub>2<\/jats:sub>\u2026, <jats:italic>G<\/jats:italic><jats:sub>n<\/jats:sub> be regular graphs and <jats:italic>H<\/jats:italic> be the Cartesian product of these graphs (<jats:italic>H<\/jats:italic> = <jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub> \u00d7 <jats:italic>G<\/jats:italic><jats:sub>2<\/jats:sub> \u00d7 \u2026 \u00d7 <jats:italic>G<\/jats:italic><jats:sub>n<\/jats:sub>). The following will be proved: If the set {<jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>G<\/jats:italic><jats:sub>2<\/jats:sub>\u2026, <jats:italic>G<\/jats:italic><jats:sub>n<\/jats:sub>} has at leat one of the following properties: (*) for at leat one <jats:italic>i<\/jats:italic> \u03f5 {1, 2,\u2026, <jats:italic>n<\/jats:italic>}, there exists a 1\u2010factorization of <jats:italic>G<\/jats:italic><jats:sub>i<\/jats:sub> or (**) there exists at least two numbers <jats:italic>i<\/jats:italic> and <jats:italic>j<\/jats:italic> such that 1 \u2264 <jats:italic>i<\/jats:italic> &lt; <jats:italic>j<\/jats:italic> \u2264 <jats:italic>n<\/jats:italic> and both the Graphs <jats:italic>G<\/jats:italic><jats:sub>i<\/jats:sub> and <jats:italic>G<\/jats:italic><jats:sub>j<\/jats:sub> contain at least one 1\u2010factor, then there exists a 1\u2010factorization of <jats:italic>H<\/jats:italic>. Further results: Let <jats:italic>F<\/jats:italic> be a cycle of length greater than three and let <jats:italic>G<\/jats:italic> be an arbitrary cubic graph. Then there exists a 1\u2010factorization of the 5\u2010regular graph <jats:italic>H<\/jats:italic> = <jats:italic>F<\/jats:italic> \u00d7 <jats:italic>G<\/jats:italic>. The last result shows that neither (*) nor (**) is a necessary condition for the existence of a 1\u2010factorization of a Cartesian product of regular graphs.<\/jats:p>","DOI":"10.1002\/jgt.3190030104","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T11:57:39Z","timestamp":1180180659000},"page":"23-34","source":"Crossref","is-referenced-by-count":18,"title":["1\u2010Factorizations of cartesian products of regular graphs"],"prefix":"10.1002","volume":"3","author":[{"given":"Anton","family":"Kotzig","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"311","article-title":"Colorations des ar\u011btes d'un graphe","volume":"15","author":"Fournier J. 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G.","year":"1964","journal-title":"Diskret. Analiz."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190030104","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190030104","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T09:37:05Z","timestamp":1699781825000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190030104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1979,3]]}},"alternative-id":["10.1002\/jgt.3190030104"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190030104","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,3]]}}}