{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T13:57:20Z","timestamp":1780408640676,"version":"3.54.1"},"reference-count":22,"publisher":"EDP Sciences","issue":"5","license":[{"start":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T00:00:00Z","timestamp":1633651200000},"content-version":"vor","delay-in-days":37,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871280, 11971349"],"award-info":[{"award-number":["11871280, 11971349"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U1811461"],"award-info":[{"award-number":["U1811461"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2020B1515310009"],"award-info":[{"award-number":["2020B1515310009"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013088","name":"Qinglan Project of Jiangsu Province of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100013088","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2021,9,15]]},"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:p>A spanning subgraph of a graph <jats:italic>G<\/jats:italic> is called a path-factor of <jats:italic>G<\/jats:italic> if its each component is a path. A path-factor is called a \ud835\udcab<jats:sub>\u2265<jats:italic>k<\/jats:italic><\/jats:sub>-factor of <jats:italic>G<\/jats:italic> if its each component admits at least <jats:italic>k<\/jats:italic> vertices, where <jats:italic>k<\/jats:italic> \u2265 2. (Zhang and Zhou, <jats:italic>Discrete Math.<\/jats:italic> <jats:bold>309<\/jats:bold> (2009) 2067\u20132076) defined the concept of \ud835\udcab<jats:sub>\u2265<jats:italic>k<\/jats:italic><\/jats:sub>-factor covered graphs, <jats:italic>i.e.<\/jats:italic>, <jats:italic>G<\/jats:italic> is called a \ud835\udcab<jats:sub>\u2265<jats:italic>k<\/jats:italic><\/jats:sub>-factor covered graph if it has a \ud835\udcab<jats:sub>\u2265<jats:italic>k<\/jats:italic><\/jats:sub>-factor covering <jats:italic>e<\/jats:italic> for any <jats:italic>e<\/jats:italic>\u2208 <jats:italic>E(G)<\/jats:italic>. In this paper, we firstly obtain a minimum degree condition for a planar graph being a \ud835\udcab<jats:sub>\u22652<\/jats:sub>-factor and \ud835\udcab<jats:sub>\u22653<\/jats:sub>-factor covered graph, respectively. Secondly, we investigate the relationship between the maximum degree of any pairs of non-adjacent vertices and \ud835\udcab<jats:sub>\u2265<jats:italic>k<\/jats:italic><\/jats:sub>-factor covered graphs, and obtain a sufficient condition for the existence of \ud835\udcab<jats:sub>\u22652<\/jats:sub>-factor and \ud835\udcab<jats:sub>\u22653<\/jats:sub>-factor covered graphs, respectively.<\/jats:p>","DOI":"10.1051\/ro\/2021140","type":"journal-article","created":{"date-parts":[[2021,9,16]],"date-time":"2021-09-16T18:53:01Z","timestamp":1631818381000},"page":"2907-2913","source":"Crossref","is-referenced-by-count":15,"title":["Some degree conditions for \ud835\udcab<sub>\u2265<i>k<\/i><\/sub>-factor covered graphs"],"prefix":"10.1051","volume":"55","author":[{"given":"Guowei","family":"Dai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zan-Bo","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yicheng","family":"Hang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8563-4958","authenticated-orcid":false,"given":"Xiaoyan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"250","published-online":{"date-parts":[[2021,10,8]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/jgt.3190090103","volume":"9","year":"1985","journal-title":"J. Graph Theory."},{"key":"R2","first-page":"97","volume":"16","year":"1980","journal-title":"TRU Math."},{"key":"R3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0012-365X(82)90048-6","volume":"42","year":"1982","journal-title":"Discrete Math."},{"key":"R4","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0012-365X(01)00214-X","volume":"243","year":"2002","journal-title":"Discrete Math."},{"key":"R5","unstructured":"Bondy J.A. and Murty U.S.R., Graph theory with applications, NewYork-Amsterdam-Oxford, North-Holland (1982)."},{"key":"R6","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0012-365X(73)90138-6","volume":"5","year":"1973","journal-title":"Discrete Math."},{"key":"R7","doi-asserted-by":"crossref","unstructured":"Dai G., The existence of path-factor covered graphs, Discuss. Math. Graph Theory. DOI: 10.7151\/dmgt.2353\n.","DOI":"10.7151\/dmgt.2353"},{"key":"R8","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1002\/jgt.22253","volume":"89","year":"2018","journal-title":"J. Graph Theory"},{"key":"R9","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0095-8956(03)00027-3","volume":"88","year":"2003","journal-title":"J. Combin. Theory Ser. B"},{"key":"R10","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1002\/1097-0118(200104)36:4<175::AID-JGT1005>3.0.CO;2-T","volume":"36","year":"2001","journal-title":"J. Graph Theory"},{"key":"R11","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.disc.2004.01.016","volume":"283","year":"2004","journal-title":"Discrete Math."},{"key":"R12","doi-asserted-by":"crossref","first-page":"551","DOI":"10.7151\/dmgt.1426","volume":"28","year":"2008","journal-title":"Discuss. Math. Graph Theory"},{"key":"R13","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1002\/jgt.10022","volume":"39","year":"2002","journal-title":"J. Graph Theory"},{"key":"R14","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1016\/j.disc.2005.11.059","volume":"307","year":"2007","journal-title":"Discrete Math."},{"key":"R15","doi-asserted-by":"crossref","first-page":"314","DOI":"10.4153\/CJM-1952-028-2","volume":"4","year":"1952","journal-title":"Canad. J. Math."},{"key":"R16","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1002\/jgt.3190180207","volume":"18","year":"1994","journal-title":"J. Graph Theory"},{"key":"R17","first-page":"225","volume":"15","year":"1973","journal-title":"J. Combin. Theory Ser. B"},{"key":"R18","first-page":"385","volume":"16","year":"2001","journal-title":"Appl. Math. J. Chinese Univ. Ser. A"},{"key":"R19","doi-asserted-by":"crossref","unstructured":"Yu Q. and Liu G., Graph Factors and Matching Extensions. Higher Education Press, Beijing (2009).","DOI":"10.1007\/978-3-540-93952-8"},{"key":"R20","doi-asserted-by":"crossref","first-page":"2067","DOI":"10.1016\/j.disc.2008.04.022","volume":"309","year":"2009","journal-title":"Discrete Math."},{"key":"R21","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1051\/ro\/2017045","volume":"53","year":"2019","journal-title":"RAIRO:OR"},{"key":"R22","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.7151\/dmgt.1974","volume":"37","year":"2017","journal-title":"Discuss. Math. Graph Theory"}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2021140\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T10:17:13Z","timestamp":1633688233000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2021140"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9]]},"references-count":22,"journal-issue":{"issue":"5"},"alternative-id":["ro200568"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2021140","relation":{},"ISSN":["0399-0559","1290-3868"],"issn-type":[{"value":"0399-0559","type":"print"},{"value":"1290-3868","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9]]}}}