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 Orthogonal matchings revisited Qu, Cunquan1; Wang, Guanghui1; Yan, Guiying2 2015-11-06 Source Publication DISCRETE MATHEMATICS ISSN 0012-365X Volume 338Issue:11Pages:2080-2088 Abstract Let G be a graph on n vertices, which is an edge-disjoint union of ms-factors, that is, s regular spanning subgraphs. Alspach first posed the problem that if there exists a matching M of m edges with exactly one edge from each 2-factor. Such a matching is called orthogonal because of applications in design theory. For s = 2, so far the best known result is due to Stong in 2002, which states that if n >= 3m-2, then there is an orthogonal matching. Anstee and Caccetta also asked if there is a matching M of m edges with exactly one edge from each s-factor? They answered yes for s >= 3. In this paper, we get a better bound and prove that if s = 2 and n >= 2 root 2m+4.5 (note that 2 root 2 <= 2.825), then there is an orthogonal matching. We also prove that if s = 1 and n >= 3.2m - 1, then there is an orthogonal matching, which improves the previous bound (3.79m). (C) 2015 Elsevier B.V. All rights reserved. Keyword Regular graphs Orthogonal matchings Rainbow matchings Factors DOI 10.1016/j.disc.2015.05.009 Language 英语 Funding Project National Natural Science Foundation of China[11101243] ; National Natural Science Foundation of China[11371355] ; Scientific Research Foundation for the Excellent Middle-Aged and Young Scientists of Shandong Province of China[BS2012SF016] ; Shandong University ; Independent Innovation Foundation of Shandong University[IFYT14012] WOS Research Area Mathematics WOS Subject Mathematics WOS ID WOS:000358459300026 Publisher ELSEVIER SCIENCE BV Citation statistics Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS] Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/20457 Collection 应用数学研究所 Affiliation 1.Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 10080, Peoples R China Recommended CitationGB/T 7714 Qu, Cunquan,Wang, Guanghui,Yan, Guiying. Orthogonal matchings revisited[J]. DISCRETE MATHEMATICS,2015,338(11):2080-2088. APA Qu, Cunquan,Wang, Guanghui,&Yan, Guiying.(2015).Orthogonal matchings revisited.DISCRETE MATHEMATICS,338(11),2080-2088. MLA Qu, Cunquan,et al."Orthogonal matchings revisited".DISCRETE MATHEMATICS 338.11(2015):2080-2088.
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