{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:28:06Z","timestamp":1740144486447,"version":"3.37.3"},"reference-count":20,"publisher":"EDP Sciences","issue":"6","license":[{"start":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T00:00:00Z","timestamp":1733443200000},"content-version":"vor","delay-in-days":35,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong","doi-asserted-by":"crossref","award":["2021A1515012045"],"award-info":[{"award-number":["2021A1515012045"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12161073"],"award-info":[{"award-number":["12161073"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2024,3,6]]},"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p>As a generalization of matching preclusion number of a graph, we provide the (strong) integer <jats:italic>k<\/jats:italic>-matching preclusion number, abbreviated as <jats:italic>MP<jats:sup>k<\/jats:sup><\/jats:italic> number (<jats:italic>SMP<jats:sup>k<\/jats:sup><\/jats:italic> number), which is the minimum number of edges (vertices and edges) whose deletion results in a graph that has neither perfect integer <jats:italic>k<\/jats:italic>-matching nor almost perfect integer <jats:italic>k<\/jats:italic>-matching. In this paper, we obtain a necessary condition of graphs with an almost-perfect integer <jats:italic>k<\/jats:italic>-matching and a relational expression between the matching number and the integer <jats:italic>k<\/jats:italic>-matching number of bipartite graphs. And then the <jats:italic>MP<jats:sup>k<\/jats:sup><\/jats:italic> number and the <jats:italic>SMP<jats:sup>k<\/jats:sup><\/jats:italic> number of complete graphs, bipartite graphs and arrangement graphs are obtained, respectively.<\/jats:p>","DOI":"10.1051\/ro\/2024064","type":"journal-article","created":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T09:01:11Z","timestamp":1710147671000},"page":"5369-5380","source":"Crossref","is-referenced-by-count":0,"title":["Integer <i>k<\/i>-matching preclusion of graphs"],"prefix":"10.1051","volume":"58","author":[{"given":"Caibing","family":"Chang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2024,12,6]]},"reference":[{"key":"R1","unstructured":"Akers S., Harel D. and Krishnamurthy B., The star graph: an attractive alternative to the n-cube. 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