{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:16:17Z","timestamp":1740104177113,"version":"3.37.3"},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T00:00:00Z","timestamp":1562889600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2020,1]]},"abstract":"Abstract<\/jats:title>This paper focuses on graph decompositions of , the \u2010partite multigraph in which each part has size , where two vertices in the same part or different parts are joined by exactly edges or edges respectively. Assuming one condition, necessary and sufficient conditions are found to embed a k<\/jats:italic>\u2010edge\u2010coloring of into a Hamiltonian decomposition of . In the tightest case, this assumption is in fact proved to be a new necessary condition. Unlike previous results, of particular interest here is a necessary condition involving the existence of certain components in a related bipartite graph.<\/jats:p>","DOI":"10.1002\/jgt.22468","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T12:21:28Z","timestamp":1562934088000},"page":"49-63","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Embedding an edge\u2010coloring of K(nr;\u03bb1,\u03bb2) into a Hamiltonian decomposition of K(nr+2;\u03bb1,\u03bb2)"],"prefix":"10.1002","volume":"93","author":[{"given":"Mustafa","family":"Demir","sequence":"first","affiliation":[{"name":"Department of Mathematics Kastamonu University Kastamonu Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7324-0465","authenticated-orcid":false,"given":"C. A.","family":"Rodger","sequence":"additional","affiliation":[{"name":"Department of Mathematics Kastamonu University Kastamonu Turkey"}]}],"member":"311","published-online":{"date-parts":[[2019,7,12]]},"reference":[{"key":"e_1_2_4_1_2_1","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-26.1.21"},{"key":"e_1_2_4_1_3_1","first-page":"19","article-title":"Small embeddings of incomplete idempotent Latin squares","volume":"17","author":"Andersen L. D.","year":"1983","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_4_1_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20617"},{"key":"e_1_2_4_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-012-1164-0"},{"key":"e_1_2_4_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579280"},{"key":"e_1_2_4_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(84)90020-0"},{"key":"e_1_2_4_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(86)90186-X"},{"key":"e_1_2_4_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(76)90039-X"},{"volume-title":"R\u00e9cr\u00e9ations math\u00e9matiques","year":"1883","author":"Lucas E.","key":"e_1_2_4_1_10_1"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.22468","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22468","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/jgt.22468","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22468","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T10:26:07Z","timestamp":1694082367000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.22468"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,12]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1002\/jgt.22468"],"URL":"https:\/\/doi.org\/10.1002\/jgt.22468","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"type":"print","value":"0364-9024"},{"type":"electronic","value":"1097-0118"}],"subject":[],"published":{"date-parts":[[2019,7,12]]},"assertion":[{"value":"2017-12-04","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-05-15","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-07-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}