{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T14:53:14Z","timestamp":1778597594994,"version":"3.51.4"},"reference-count":14,"publisher":"EDP Sciences","issue":"6","license":[{"start":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T00:00:00Z","timestamp":1733443200000},"content-version":"vor","delay-in-days":35,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["12061047"],"award-info":[{"award-number":["12061047"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004479","name":"Natural Science Foundation of Jiangxi Province","doi-asserted-by":"publisher","award":["20212BAB201027"],"award-info":[{"award-number":["20212BAB201027"]}],"id":[{"id":"10.13039\/501100004479","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004479","name":"Natural Science Foundation of Jiangxi Province","doi-asserted-by":"publisher","award":["20192BAB211002"],"award-info":[{"award-number":["20192BAB211002"]}],"id":[{"id":"10.13039\/501100004479","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2024,10,27]]},"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p>Ruskey and Savage asked the following question: Does every matching in <jats:italic>Q<jats:sub>n<\/jats:sub><\/jats:italic> for <jats:italic>n \u2265<\/jats:italic> 2 extend to a Hamiltonian cycle of <jats:italic>Q<jats:sub>n<\/jats:sub><\/jats:italic>? Kreweras conjectured that every perfect matching of <jats:italic>Q<jats:sub>n<\/jats:sub><\/jats:italic> for <jats:italic>n \u2265<\/jats:italic> 2 can be extended to a Hamiltonian cycle of <jats:italic>Q<jats:sub>n<\/jats:sub><\/jats:italic>. Fink confirmed the conjecture. An edge in <jats:italic>Q<jats:sub>n<\/jats:sub><\/jats:italic> is an edge of direction <jats:italic>i<\/jats:italic> if its endpoints differ in the <jats:italic>i<\/jats:italic>th position. So all the edges of <jats:italic>Q<jats:sub>n<\/jats:sub><\/jats:italic> can be divided into <jats:italic>n<\/jats:italic> directions, <jats:italic>i.e<\/jats:italic>., edges of direction 1, \u2026, edges of direction <jats:italic>n<\/jats:italic>. The set of all edges of direction <jats:italic>i<\/jats:italic> of <jats:italic>Q<jats:sub>n<\/jats:sub><\/jats:italic> is denoted by <jats:italic>E<jats:sub>i<\/jats:sub><\/jats:italic>. In this paper, we obtain the following result. For <jats:italic>n \u2265<\/jats:italic> 6, let <jats:italic>M<\/jats:italic> be a matching in <jats:italic>Q<jats:sub>n<\/jats:sub><\/jats:italic> with <jats:italic>|M|<\/jats:italic> &lt; 10 <jats:italic>\u00d7<\/jats:italic> 2<jats:sup><jats:italic>n<\/jats:italic>\u22125<\/jats:sup>. If <jats:italic>M<\/jats:italic> contains edges in at most 5 directions, then <jats:italic>M<\/jats:italic> can be extended to a Hamiltonian cycle of <jats:italic>Q<jats:sub>n<\/jats:sub><\/jats:italic>.<\/jats:p>","DOI":"10.1051\/ro\/2024210","type":"journal-article","created":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T19:47:04Z","timestamp":1730231224000},"page":"5237-5254","source":"Crossref","is-referenced-by-count":4,"title":["A kind of matchings extend to Hamiltonian cycles in hypercubes"],"prefix":"10.1051","volume":"58","author":[{"given":"Shujia","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fan","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2024,12,6]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1016\/j.disc.2005.12.050","volume":"307","author":"Caha","year":"2007","journal-title":"Discrete Math."},{"key":"R2","first-page":"123","volume":"11","author":"Dimitrov","year":"2009","journal-title":"Discrete Math. Theor. Comput. Sci."},{"key":"R3","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1137\/S0895480103432805","volume":"19","author":"Dvo\u0159\u00e1k","year":"2005","journal-title":"SIAM J. Discrete Math."},{"key":"R4","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1002\/jgt.22371","volume":"90","author":"Dvo\u0159\u00e1k","year":"2019","journal-title":"J. Graph Theory"},{"key":"R5","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1016\/j.jctb.2007.02.007","volume":"97","author":"Fink","year":"2007","journal-title":"J. Comb. Theory Ser. B"},{"key":"R6","doi-asserted-by":"crossref","first-page":"1624","DOI":"10.1016\/j.ejc.2009.03.007","volume":"30","author":"Fink","year":"2009","journal-title":"Eur. J. Comb."},{"key":"R7","doi-asserted-by":"crossref","first-page":"P2.56","DOI":"10.37236\/6928","volume":"25","author":"Gregor","year":"2018","journal-title":"Electron. J. Comb."},{"key":"R8","unstructured":"Gros L., Th\u00e9orie du Baguenodier. Aim\u00e9 Vingtrinier, Lyon (1872)."},{"key":"R9","first-page":"87","volume":"16","author":"Kreweras","year":"1996","journal-title":"Bull. Inst. Comb. Appl."},{"key":"R10","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1137\/0406012","volume":"6","author":"Ruskey","year":"1993","journal-title":"SIAM J. Discrete Math."},{"key":"R11","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.disc.2013.12.014","volume":"321","author":"Wang","year":"2014","journal-title":"Discrete Math."},{"key":"R12","first-page":"269","volume":"118","author":"Wang","year":"2015","journal-title":"ARS Comb."},{"key":"R13","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/s00373-015-1533-6","volume":"32","author":"Wang","year":"2016","journal-title":"Graphs Comb."},{"key":"R14","doi-asserted-by":"crossref","first-page":"217","DOI":"10.7151\/dmgt.2010","volume":"38","author":"Wang","year":"2018","journal-title":"Discuss. Math. Graph Theory"}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2024210\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T08:51:36Z","timestamp":1733475096000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2024210"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11]]},"references-count":14,"journal-issue":{"issue":"6"},"alternative-id":["ro230630"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2024210","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"value":"0399-0559","type":"print"},{"value":"2804-7303","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11]]}}}