{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T11:48:56Z","timestamp":1725277736199},"reference-count":29,"publisher":"EDP Sciences","issue":"5","license":[{"start":{"date-parts":[[2022,9,14]],"date-time":"2022-09-14T00:00:00Z","timestamp":1663113600000},"content-version":"vor","delay-in-days":13,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2022,8,16]]},"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:p>Combining the concept of a fractional (<jats:italic>g<\/jats:italic>,\u00a0<jats:italic>f<\/jats:italic>)-covered graph with that of a fractional ID-(<jats:italic>g<\/jats:italic>,\u00a0<jats:italic>f<\/jats:italic>)-factor-critical graph, we define the concept of a fractional ID-(<jats:italic>g<\/jats:italic>,\u00a0<jats:italic>f<\/jats:italic>)-factor-critical covered graph. This paper reveals the relationship between some graph parameters and the existence of fractional ID-(<jats:italic>g<\/jats:italic>,\u00a0<jats:italic>f<\/jats:italic>)-factor-critical covered graphs. A sufficient condition for a graph being a fractional ID-(<jats:italic>g<\/jats:italic>,\u00a0<jats:italic>f<\/jats:italic>)-factor-critical covered graph is presented. In addition, we demonstrate the sharpness of the main result in this paper by constructing a special graph class. Furthermore, the relationship between other graph parameters(such as binding number, toughness, sun toughness and neighborhood union) and fractional ID-(<jats:italic>g<\/jats:italic>,\u00a0<jats:italic>f<\/jats:italic>)-factor-critical covered graphs can be studied further.<\/jats:p>","DOI":"10.1051\/ro\/2022144","type":"journal-article","created":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T18:53:10Z","timestamp":1661367190000},"page":"3257-3265","source":"Crossref","is-referenced-by-count":2,"title":["Sharp conditions on fractional ID-(<i>g<\/i>,\u00a0<i>f<\/i>)-factor-critical covered graphs"],"prefix":"10.1051","volume":"56","author":[{"given":"Hongxia","family":"Liu","sequence":"first","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2022,9,14]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1007\/s10255-014-0411-y","volume":"30","author":"Cai","year":"2014","journal-title":"Acta Math. Appl. Sin. Engl. 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