{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T12:41:19Z","timestamp":1774528879713,"version":"3.50.1"},"reference-count":21,"publisher":"EDP Sciences","issue":"3","license":[{"start":{"date-parts":[[2023,5,18]],"date-time":"2023-05-18T00:00:00Z","timestamp":1684368000000},"content-version":"vor","delay-in-days":17,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"SCience&Technology development Fund of Tianjin Education Commission for Higher Education","award":["2019KJ090"],"award-info":[{"award-number":["2019KJ090"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2023,4,14]]},"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:p>Let $ \\mathcal{L}$ be a set which consists of some connected graphs. Let<jats:italic>E<\/jats:italic>be a spanning subgraph of graph<jats:italic>G<\/jats:italic>. It is called a $ \\mathcal{L}$-factor if every component of it is isomorphic to the element in $ \\mathcal{L}$. In this contribution, we give the lower bounds of four parameters (<jats:italic>t<\/jats:italic>(<jats:italic>G<\/jats:italic>),\u00a0<jats:italic>I<\/jats:italic>(<jats:italic>G<\/jats:italic>),\u00a0<jats:italic>I<\/jats:italic>\u2032(<jats:italic>G<\/jats:italic>),bind (<jats:italic>G<\/jats:italic>)) of<jats:italic>G<\/jats:italic>, which force the graph<jats:italic>G<\/jats:italic>admits a ({<jats:italic>K<\/jats:italic><jats:sub>1,<jats:italic>i<\/jats:italic><\/jats:sub>:<jats:italic>q<\/jats:italic>\u00a0\u2264\u00a0<jats:italic>i<\/jats:italic>\u00a0\u2264\u00a02<jats:italic>q<\/jats:italic>\u00a0\u2212\u00a01}\u00a0\u222a\u00a0{<jats:italic>K<\/jats:italic><jats:sub>2<jats:italic>q<\/jats:italic>+1<\/jats:sub>})-factor for<jats:italic>q<\/jats:italic>\u00a0\u2265\u00a02 and a {<jats:italic>P<\/jats:italic><jats:sub>2<\/jats:sub>,\u00a0<jats:italic>P<\/jats:italic><jats:sub>2<jats:italic>q<\/jats:italic>+1<\/jats:sub>}-factor for<jats:italic>q<\/jats:italic>\u00a0\u2265\u00a03 respectively. The tightness of the bounds are given.<\/jats:p>","DOI":"10.1051\/ro\/2023057","type":"journal-article","created":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T19:11:40Z","timestamp":1681758700000},"page":"1167-1177","source":"Crossref","is-referenced-by-count":1,"title":["Toughness and binding number bounds of star-like and path factor"],"prefix":"10.1051","volume":"57","author":[{"given":"Xinge","family":"Feng","sequence":"first","affiliation":[]},{"given":"Xingchao","family":"Deng","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2023,5,18]]},"reference":[{"key":"R1","first-page":"183","volume":"10","author":"Anderson","year":"1971","journal-title":"J. Graph Theory"},{"key":"R2","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1002\/int.22233","volume":"35","author":"Abdullah","year":"2020","journal-title":"Int. J. Intell. 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