{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T20:20:39Z","timestamp":1772050839268,"version":"3.50.1"},"reference-count":21,"publisher":"EDP Sciences","issue":"3","license":[{"start":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T00:00:00Z","timestamp":1560470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.edpsciences.org\/en\/authors\/copyright-and-licensing"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2017,5,26]]},"published-print":{"date-parts":[[2019,7]]},"abstract":"<jats:p>For a set  \u210b of connected graphs, a spanning subgraph <jats:italic>H<\/jats:italic> of a graph <jats:italic>G<\/jats:italic> is called an \n\u210b-factor of <jats:italic>G<\/jats:italic> if every component of <jats:italic>H<\/jats:italic> is isomorphic to a member of\u210b. An <jats:italic>H<\/jats:italic>-factor is also referred as a component factor. If each component of <jats:italic>H<\/jats:italic> is a star (resp. path), <jats:italic>H<\/jats:italic> is called a star (resp. path) factor. By a <jats:italic>P<\/jats:italic><jats:sub>\u2265\u00a0<jats:italic>k<\/jats:italic><\/jats:sub>-factor (<jats:italic>k<\/jats:italic> positive integer) we mean a path factor in which each component path has at least <jats:italic>k<\/jats:italic> vertices (<jats:italic>i.e.<\/jats:italic> it has length at least <jats:italic>k<\/jats:italic>\u00a0\u2212\u00a01). A graph <jats:italic>G<\/jats:italic> is called a <jats:italic>P<\/jats:italic><jats:sub>\u2265\u00a0<jats:italic>k<\/jats:italic><\/jats:sub>-factor covered graph, if for each edge <jats:italic>e<\/jats:italic> of <jats:italic>G<\/jats:italic>, there is a <jats:italic>P<\/jats:italic><jats:sub>\u2265\u00a0<jats:italic>k<\/jats:italic><\/jats:sub>-factor covering <jats:italic>e<\/jats:italic>. In this paper, we prove that (1) a graph <jats:italic>G<\/jats:italic> has a {<jats:italic>K<\/jats:italic><jats:sub>1,1<\/jats:sub>,<jats:italic>K<\/jats:italic><jats:sub>1,2<\/jats:sub>,\u00a0\u2026\u00a0,<jats:italic>K<\/jats:italic><jats:sub>1,<jats:italic>k<\/jats:italic><\/jats:sub>}-factor if and only if bind(<jats:italic>G<\/jats:italic>) \u2265 1\/<jats:italic>k<\/jats:italic>, \nwhere <jats:italic>k<\/jats:italic>\u00a0\u2265\u00a02 is an integer; (2) a connected graph <jats:italic>G<\/jats:italic> is a <jats:italic>P<\/jats:italic><jats:sub>\u2265\u00a02<\/jats:sub>-factor covered graph if \nbind(<jats:italic>G<\/jats:italic>) &gt; 2\/3; (3) a connected graph <jats:italic>G<\/jats:italic> is a <jats:italic>P<\/jats:italic><jats:sub>\u2265\u00a03<\/jats:sub>-factor covered graph if \n bind(<jats:italic>G<\/jats:italic>) \u2265 3\/2. Furthermore, it is shown that the results in this paper are best possible in some sense.<\/jats:p>","DOI":"10.1051\/ro\/2017045","type":"journal-article","created":{"date-parts":[[2017,5,29]],"date-time":"2017-05-29T18:35:34Z","timestamp":1496082934000},"page":"723-730","source":"Crossref","is-referenced-by-count":42,"title":["Some results about component factors in graphs"],"prefix":"10.1051","volume":"53","author":[{"given":"Sizhong","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2019,6,14]]},"reference":[{"key":"R1","unstructured":"Anderson I., Binding numbers of graphs: a survey. 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