{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T09:06:36Z","timestamp":1761901596995,"version":"build-2065373602"},"reference-count":33,"publisher":"EDP Sciences","issue":"5","license":[{"start":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T00:00:00Z","timestamp":1761868800000},"content-version":"vor","delay-in-days":60,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20241949"],"award-info":[{"award-number":["BK20241949"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2023MA078"],"award-info":[{"award-number":["ZR2023MA078"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2025,9,10]]},"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>\n                    Let\n                    <jats:italic>G<\/jats:italic>\n                    denote a graph and\n                    <jats:italic>k<\/jats:italic>\n                    \u2265 2 be an integer. A {\n                    <jats:italic>K<\/jats:italic>\n                    <jats:sub>1,1<\/jats:sub>\n                    ,\n                    <jats:italic>K<\/jats:italic>\n                    <jats:sub>1,2<\/jats:sub>\n                    , . . . ,\n                    <jats:italic>K<\/jats:italic>\n                    <jats:sub>\n                      1,\n                      <jats:italic>k<\/jats:italic>\n                    <\/jats:sub>\n                    ,\n                    <jats:italic>\u03a4<\/jats:italic>\n                    (2\n                    <jats:italic>k<\/jats:italic>\n                    + 1)}-factor of\n                    <jats:italic>G<\/jats:italic>\n                    is a spanning subgraph, whose every connected component is isomorphic to an element of {\n                    <jats:italic>K<\/jats:italic>\n                    <jats:sub>1,1<\/jats:sub>\n                    ,\n                    <jats:italic>K<\/jats:italic>\n                    <jats:sub>1,2<\/jats:sub>\n                    , . . . ,\n                    <jats:italic>K<\/jats:italic>\n                    <jats:sub>\n                      1,\n                      <jats:italic>k<\/jats:italic>\n                    <\/jats:sub>\n                    ,\n                    <jats:italic>\u03a4<\/jats:italic>\n                    (2\n                    <jats:italic>k<\/jats:italic>\n                    + 1)}, where\n                    <jats:italic>\u03a4<\/jats:italic>\n                    (2\n                    <jats:italic>k<\/jats:italic>\n                    + 1) is a special family of trees. In this paper, we put forward some sufficient conditions for the existence of {\n                    <jats:italic>K<\/jats:italic>\n                    <jats:sub>1,1<\/jats:sub>\n                    ,\n                    <jats:italic>K<\/jats:italic>\n                    <jats:sub>1,2<\/jats:sub>\n                    , . . . ,\n                    <jats:italic>K<\/jats:italic>\n                    <jats:sub>\n                      1,\n                      <jats:italic>k<\/jats:italic>\n                    <\/jats:sub>\n                    ,\n                    <jats:italic>\u03a4<\/jats:italic>\n                    (2\n                    <jats:italic>k<\/jats:italic>\n                    + 1)}-factors in graphs. Furthermore, we construct some extremal graphs to show that the main results in this paper are best possible.\n                  <\/jats:p>","DOI":"10.1051\/ro\/2025127","type":"journal-article","created":{"date-parts":[[2025,9,12]],"date-time":"2025-09-12T18:47:36Z","timestamp":1757702856000},"page":"3241-3252","source":"Crossref","is-referenced-by-count":0,"title":["Some sufficient conditions for graphs to have component factors"],"prefix":"10.1051","volume":"59","author":[{"given":"Sizhong","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Science, Jiangsu University of Science and Technology","place":["P.R. China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2025,10,31]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0012-365X(82)90048-6","volume":"42","author":"Amahashi","year":"1982","journal-title":"Discrete Math."},{"key":"R2","doi-asserted-by":"crossref","first-page":"4392","DOI":"10.1002\/int.22464","volume":"36","author":"Gao","year":"2021","journal-title":"Int. J. Intell. Syst."},{"key":"R3","doi-asserted-by":"crossref","first-page":"114008","DOI":"10.1016\/j.disc.2024.114008","volume":"347","author":"Gao","year":"2024","journal-title":"Discrete Math."},{"key":"R4","doi-asserted-by":"crossref","first-page":"103468","DOI":"10.1016\/j.ejc.2021.103468","volume":"101","author":"Gu","year":"2022","journal-title":"Eur. J. Comb."},{"key":"R5","doi-asserted-by":"crossref","first-page":"2005","DOI":"10.1016\/j.disc.2012.03.017","volume":"312","author":"Kano","year":"2012","journal-title":"Discrete Math."},{"key":"R6","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.aml.2009.11.003","volume":"23","author":"Kano","year":"2010","journal-title":"Appl. Math. Lett."},{"doi-asserted-by":"crossref","unstructured":"Kano M., Lu H. and Yu Q., Fractional factors, component factors and isolated vertex conditions in graphs. Electron. J. Comb. 26 (2019) #P4.33.","key":"R7","DOI":"10.37236\/8498"},{"key":"R8","doi-asserted-by":"crossref","first-page":"111906","DOI":"10.1016\/j.disc.2020.111906","volume":"343","author":"Kim","year":"2020","journal-title":"Discrete Math."},{"key":"R9","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1007\/s00373-020-02266-6","volume":"37","author":"Klopp","year":"2021","journal-title":"Graphs Comb."},{"key":"R10","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1002\/jgt.20008","volume":"46","author":"Kouider","year":"2004","journal-title":"J. Graph Theory"},{"key":"R11","doi-asserted-by":"crossref","first-page":"112588","DOI":"10.1016\/j.disc.2021.112588","volume":"344","author":"Li","year":"2021","journal-title":"Discrete Math."},{"key":"R12","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.dam.2024.07.043","volume":"359","author":"Liu","year":"2024","journal-title":"Discrete Appl. Math."},{"key":"R13","doi-asserted-by":"crossref","first-page":"3315","DOI":"10.2298\/FIL2310315L","volume":"37","author":"Lv","year":"2023","journal-title":"Filomat"},{"key":"R14","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1016\/j.laa.2020.06.004","volume":"614","author":"O","year":"2021","journal-title":"Linear Algebra App."},{"key":"R15","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1002\/jgt.22789","volume":"100","author":"O","year":"2022","journal-title":"J. Graph Theory"},{"key":"R16","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1090\/S0002-9939-1953-0063009-7","volume":"4","author":"Tutte","year":"1953","journal-title":"Proc. Amer. Math. Soc."},{"key":"R17","first-page":"4579","volume":"39","author":"Wang","year":"2025","journal-title":"Filomat"},{"key":"R18","doi-asserted-by":"crossref","first-page":"4317","DOI":"10.1051\/ro\/2022208","volume":"56","author":"Wu","year":"2022","journal-title":"RAIRO Oper. Res."},{"key":"R19","doi-asserted-by":"crossref","first-page":"2177","DOI":"10.2298\/FIL2406177W","volume":"38","author":"Wu","year":"2024","journal-title":"Filomat"},{"key":"R20","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.1007\/s00010-024-01112-x","volume":"98","author":"Wu","year":"2024","journal-title":"Aequ. Math."},{"key":"R21","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.dam.2025.03.014","volume":"369","author":"Zhou","year":"2025","journal-title":"Discrete Appl. Math."},{"key":"R22","first-page":"601","volume":"62","author":"Zhou","year":"2025","journal-title":"J. Korean Math. Soc."},{"key":"R23","doi-asserted-by":"crossref","first-page":"23357","DOI":"10.1007\/s11227-024-06355-8","volume":"80","author":"Zhou","year":"2024","journal-title":"J. Supercomput."},{"key":"R24","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.dam.2025.06.017","volume":"376","author":"Zhou","year":"2025","journal-title":"Discrete Appl. Math."},{"key":"R25","doi-asserted-by":"crossref","first-page":"649","DOI":"10.2298\/FIL2502649Z","volume":"39","author":"Zhou","year":"2025","journal-title":"Filomat"},{"key":"R26","doi-asserted-by":"crossref","first-page":"11","DOI":"10.59277\/PRA-SER.A.24.1.02","volume":"24","author":"Zhou","year":"2023","journal-title":"Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci."},{"key":"R27","doi-asserted-by":"crossref","first-page":"7235","DOI":"10.2298\/FIL2420235Z","volume":"38","author":"Zhou","year":"2024","journal-title":"Filomat"},{"key":"R28","doi-asserted-by":"crossref","first-page":"113927","DOI":"10.1016\/j.disc.2024.113927","volume":"347","author":"Zhou","year":"2024","journal-title":"Discrete Math."},{"key":"R29","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1007\/s00010-024-01075-z","volume":"98","author":"Zhou","year":"2024","journal-title":"Aequ. Math."},{"key":"R30","doi-asserted-by":"crossref","first-page":"154","DOI":"10.55016\/ojs\/cdm.v19i3.72597","volume":"19","author":"Zhou","year":"2024","journal-title":"Contrib. Discrete Math."},{"key":"R31","doi-asserted-by":"crossref","first-page":"5885","DOI":"10.2298\/FIL2416885Z","volume":"38","author":"Zhou","year":"2024","journal-title":"Filomat"},{"key":"R32","doi-asserted-by":"crossref","first-page":"113940","DOI":"10.1016\/j.disc.2024.113940","volume":"347","author":"Zhou","year":"2024","journal-title":"Discrete Math."},{"key":"R33","doi-asserted-by":"crossref","first-page":"2711","DOI":"10.2298\/FIL2508711Z","volume":"39","author":"Zhou","year":"2025","journal-title":"Filomat"}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2025127\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T08:51:02Z","timestamp":1761900662000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2025127"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":33,"journal-issue":{"issue":"5"},"alternative-id":["ro240805"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2025127","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"type":"print","value":"0399-0559"},{"type":"electronic","value":"2804-7303"}],"subject":[],"published":{"date-parts":[[2025,9]]}}}