{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T11:09:03Z","timestamp":1778152143491,"version":"3.51.4"},"reference-count":28,"publisher":"EDP Sciences","issue":"4","license":[{"start":{"date-parts":[[2022,8,30]],"date-time":"2022-08-30T00:00:00Z","timestamp":1661817600000},"content-version":"vor","delay-in-days":60,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2022,8,9]]},"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:p>A path-factor is a spanning subgraph<jats:italic>F<\/jats:italic>of<jats:italic>G<\/jats:italic>such that every component of<jats:italic>F<\/jats:italic>is a path with at least two vertices. Let<jats:italic>k<\/jats:italic>\u00a0\u2265\u00a02 be an integer. A<jats:italic>P<\/jats:italic><jats:sub>\u2265<jats:italic>k<\/jats:italic><\/jats:sub>-factor of<jats:italic>G<\/jats:italic>means a path factor in which each component is a path with at least<jats:italic>k<\/jats:italic>vertices. A graph<jats:italic>G<\/jats:italic>is a<jats:italic>P<\/jats:italic><jats:sub>\u2265<jats:italic>k<\/jats:italic><\/jats:sub>-factor covered graph if for any<jats:italic>e<\/jats:italic>\u00a0\u2208\u00a0<jats:italic>E<\/jats:italic>(<jats:italic>G<\/jats:italic>),<jats:italic>G<\/jats:italic>has a<jats:italic>P<\/jats:italic><jats:sub>\u2265<jats:italic>k<\/jats:italic><\/jats:sub>-factor covering<jats:italic>e<\/jats:italic>. A graph<jats:italic>G<\/jats:italic>is called a<jats:italic>P<\/jats:italic><jats:sub>\u2265<jats:italic>k<\/jats:italic><\/jats:sub>-factor uniform graph if for any<jats:italic>e<\/jats:italic><jats:sub>1<\/jats:sub>,\u00a0<jats:italic>e<\/jats:italic><jats:sub>2<\/jats:sub>\u00a0\u2208\u00a0<jats:italic>E<\/jats:italic>(<jats:italic>G<\/jats:italic>) with<jats:italic>e<\/jats:italic><jats:sub>1<\/jats:sub>\u00a0\u2260\u00a0<jats:italic>e<\/jats:italic><jats:sub>2<\/jats:sub>,<jats:italic>G<\/jats:italic>has a<jats:italic>P<\/jats:italic><jats:sub>\u2265<jats:italic>k<\/jats:italic><\/jats:sub>-factor covering<jats:italic>e<\/jats:italic><jats:sub>1<\/jats:sub>and avoiding<jats:italic>e<\/jats:italic><jats:sub>2<\/jats:sub>. In other words, a graph<jats:italic>G<\/jats:italic>is called a<jats:italic>P<\/jats:italic><jats:sub>\u2265<jats:italic>k<\/jats:italic><\/jats:sub>-factor uniform graph if for any<jats:italic>e<\/jats:italic>\u00a0\u2208\u00a0<jats:italic>E<\/jats:italic>(<jats:italic>G<\/jats:italic>),<jats:italic>G<\/jats:italic>\u00a0\u2212\u00a0<jats:italic>e<\/jats:italic>is a<jats:italic>P<\/jats:italic><jats:sub>\u2265<jats:italic>k<\/jats:italic><\/jats:sub>-factor covered graph. In this paper, we present two sufficient conditions for graphs to be<jats:italic>P<\/jats:italic><jats:sub>\u22653<\/jats:sub>-factor uniform graphs depending on binding number and degree conditions. Furthermore, we show that two results are best possible in some sense.<\/jats:p>","DOI":"10.1051\/ro\/2022143","type":"journal-article","created":{"date-parts":[[2022,8,11]],"date-time":"2022-08-11T18:56:27Z","timestamp":1660244187000},"page":"2919-2927","source":"Crossref","is-referenced-by-count":19,"title":["The existence of path-factor uniform graphs with large connectivity"],"prefix":"10.1051","volume":"56","author":[{"given":"Sizhong","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiuxiang","family":"Bian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2022,8,30]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/S0304-3975(00)00247-4","volume":"263","author":"Bazgan","year":"2001","journal-title":"Theor. Comput. 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