{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T17:48:17Z","timestamp":1648662497136},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:p> A 2-factorization {F<jats:sub>1<\/jats:sub>, F<jats:sub>2<\/jats:sub>,\u2026,F<jats:sub>d<\/jats:sub>} of a 2d-regular graph G such that each [Formula: see text] and the remaining F<jats:sub>i<\/jats:sub>'s are all Hamilton cycles is called Hamilton cycle rich 2-factorization of G, where G<jats:sub>i<\/jats:sub>'s are the given non-isomorphic 2-factors of G. In this paper, we prove that there exists a 2-factorization {F<jats:sub>1<\/jats:sub>, F<jats:sub>2<\/jats:sub>,\u2026,F<jats:sub>n<\/jats:sub>} of K<jats:sub>2n,2n<\/jats:sub> such that F<jats:sub>1<\/jats:sub> \u2245 G<jats:sub>1<\/jats:sub>, F<jats:sub>2<\/jats:sub> \u2245 G<jats:sub>2<\/jats:sub> and the remaining F<jats:sub>i<\/jats:sub>'s are Hamilton cycles of K<jats:sub>2n,2n<\/jats:sub>, where G<jats:sub>1<\/jats:sub> and G<jats:sub>2<\/jats:sub> are the given two non-isomorphic 2-factors of K<jats:sub>2n,2n<\/jats:sub>. In fact our result together with the earlier results settles the existence of Hamilton cycle rich 2-factorizations of K(m, p), the complete p-partite graph with m vertices in each partite set, except when (m, p) = (2n + 1, 2), in the case that two of the 2-factors are isomorphic to the given two non-isomorphic 2-factors and the remaining are Hamilton cycles. <\/jats:p>","DOI":"10.1142\/s1793830915500263","type":"journal-article","created":{"date-parts":[[2015,6,4]],"date-time":"2015-06-04T04:18:25Z","timestamp":1433391505000},"page":"1550026","source":"Crossref","is-referenced-by-count":0,"title":["Hamilton cycle rich 2-factorization of complete bipartite graphs"],"prefix":"10.1142","volume":"07","author":[{"given":"R.","family":"Sangeetha","sequence":"first","affiliation":[{"name":"Department of Mathematics, A.V.V.M. Sri Pushpam College, Poondi, Thanjavur Dt., Tamil Nadu, India"}]},{"given":"A.","family":"Muthusamy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Periyar University, Salem, Tamilnadu, India"}]}],"member":"219","published-online":{"date-parts":[[2015,9,29]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1002\/jcd.20005"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20538"},{"key":"rf3","first-page":"331","volume":"31","author":"Bryant D.","year":"2005","journal-title":"Aust. J. Combin."},{"key":"rf4","unstructured":"D.\u00a0Bryant and C. A.\u00a0Rodger, The CRC Handbook of Combinatorial Designs, 2nd edn., eds. C. J.\u00a0Colbourn and J. H.\u00a0Dinitz (CRC Press, Boca Raton, 2007)\u00a0pp. 373\u2013382."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2009.03.003"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1002\/jcd.20163"},{"key":"rf8","first-page":"95","volume":"74","author":"Deza A.","year":"2010","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"rf9","first-page":"111","volume":"17","author":"Franek F.","year":"1995","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"rf10","unstructured":"R. K.\u00a0Guy, Combinatorial Mathematics and its Applications, ed. D. J. A.\u00a0Welsh (Academic Press, New York, 1971)\u00a0p. 121."},{"key":"rf11","first-page":"227","volume":"27","author":"Haggkvist R.","year":"1985","journal-title":"Ann. Discrete Math."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1002\/jcd.1024"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-008-0763-2"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-004-0573-0"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-011-1083-5"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830915500263","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:01:49Z","timestamp":1565186509000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830915500263"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9]]},"references-count":14,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2015,9,29]]},"published-print":{"date-parts":[[2015,9]]}},"alternative-id":["10.1142\/S1793830915500263"],"URL":"https:\/\/doi.org\/10.1142\/s1793830915500263","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9]]}}}