{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:27:59Z","timestamp":1777645679469,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T00:00:00Z","timestamp":1709769600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2024,3,7]]},"abstract":"<jats:p>\n                    Let \ud835\udc9c be a set of connected graphs. Then a spanning subgraph A of G is called an \ud835\udc9c-factor if each component of A is isomorphic to some member of \ud835\udc9c. Especially, when every graph in \ud835\udc9c is a path, A is a path factor. For a positive integer d \u2265 2, we write \ud835\udcab\n                    <jats:sub>\u2265 d<\/jats:sub>\n                    = {\ud835\udcab\n                    <jats:sub>i<\/jats:sub>\n                    | i \u2265 d}. Then a \ud835\udcab\n                    <jats:sub>\u2265 d<\/jats:sub>\n                    -factor means a path factor in which every component admits at least d vertices. A graph G is called a (\ud835\udcab\n                    <jats:sub>\u2265 d<\/jats:sub>\n                    , m)-factor deleted graph if G \u2013 E\u2032 admits a \ud835\udcab\n                    <jats:sub>\u2265 d<\/jats:sub>\n                    -factor for any E\u2032 \u2286 E( G) with | E\u2032| = m. A graph G is called a (\ud835\udcab\n                    <jats:sub>\u2265 d<\/jats:sub>\n                    , k)-factor critical graph if G \u2013 Q has a \ud835\udcab\n                    <jats:sub>\u2265 d<\/jats:sub>\n                    -factor for any Q \u2286 V ( G) with | Q| = k. In this paper, we present two degree conditions for graphs to be (\ud835\udcab\n                    <jats:sub>\u22653<\/jats:sub>\n                    , m)-factor deleted graphs and (\ud835\udcab\n                    <jats:sub>\u22653<\/jats:sub>\n                    , k)-factor critical graphs. Furthermore, we show that the two results are best possible in some sense.\n                  <\/jats:p>","DOI":"10.3233\/fi-242172","type":"journal-article","created":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T10:14:44Z","timestamp":1709892884000},"page":"67-77","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Two Sufficient Conditions for Graphs to Admit Path Factors"],"prefix":"10.1177","volume":"191","author":[{"given":"Sizhong","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, China. ,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiancheng","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, China. ,"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2024,3,7]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-242172","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-242172","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:32:58Z","timestamp":1777444378000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-242172"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,7]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,3,7]]}},"alternative-id":["10.3233\/FI-242172"],"URL":"https:\/\/doi.org\/10.3233\/fi-242172","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,7]]}}}