{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T03:34:05Z","timestamp":1773113645184,"version":"3.50.1"},"reference-count":26,"publisher":"EDP Sciences","issue":"5","license":[{"start":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T00:00:00Z","timestamp":1729468800000},"content-version":"vor","delay-in-days":50,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"crossref","award":["12201408"],"award-info":[{"award-number":["12201408"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271362"],"award-info":[{"award-number":["12271362"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2024,9,13]]},"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p>A spanning subgraph <jats:italic>H<\/jats:italic> of a graph <jats:italic>G<\/jats:italic> is called a path-factor if every component of <jats:italic>H<\/jats:italic> is a path. Wang and Zhang [<jats:italic>RAIRO:RO<\/jats:italic> 57 (2023) 2231\u20132237] conjectured that a connected graph <jats:italic>G<\/jats:italic> with <jats:italic>\u03b4<\/jats:italic>(<jats:italic>G<\/jats:italic>) \u2265 5 contains a {<jats:italic>P<\/jats:italic><jats:sub>2<\/jats:sub>, <jats:italic>P<\/jats:italic><jats:sub>5<\/jats:sub>}-factor if <jats:italic>\u03b4<\/jats:italic>(<jats:italic>G<\/jats:italic>)\u22653<jats:italic>\u03b1<\/jats:italic>(<jats:italic>G<\/jats:italic>)\u221214, where <jats:italic>\u03b4<\/jats:italic>(<jats:italic>G<\/jats:italic>) and <jats:italic>\u03b1<\/jats:italic>(<jats:italic>G<\/jats:italic>) denote the minimum degree and independence number of <jats:italic>G<\/jats:italic>, respectively. We show that the conjecture is true except <jats:italic>G<\/jats:italic> <jats:italic>\u2245<\/jats:italic> <jats:italic>X<\/jats:italic> \u2228 7<jats:italic>K<\/jats:italic><jats:sub>3<\/jats:sub>, where <jats:italic>X<\/jats:italic> is a spanning subgraph of <jats:italic>K<\/jats:italic><jats:sub>3<\/jats:sub>. Furthermore, we give two degree conditions for the existence of {<jats:italic>P<\/jats:italic><jats:sub>2<\/jats:sub>, <jats:italic>P<\/jats:italic><jats:sub>5<\/jats:sub>}-factors, one of which is a stronger version of Wang\u2019s another conjecture. We also show the degree conditions are best possible.<\/jats:p>","DOI":"10.1051\/ro\/2024184","type":"journal-article","created":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T11:46:08Z","timestamp":1726487168000},"page":"4521-4530","source":"Crossref","is-referenced-by-count":3,"title":["Degree conditions for path-factors in graphs"],"prefix":"10.1051","volume":"58","author":[{"given":"Ping","family":"Zhang","sequence":"first","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2024,10,21]]},"reference":[{"key":"R1","first-page":"97","volume":"16","author":"Akiyama","year":"1980","journal-title":"TRU Math."},{"key":"R2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/jgt.3190090103","volume":"9","author":"Akiyama","year":"1985","journal-title":"J. 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