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In this note, we determine the maximum number of independent sets of size in \u2010vertex \u2010covered graphs and classify the extremal graphs. The result answers a question proposed by Chakraborti and Loh. The proof uses an edge\u2010switching operation on hypergraphs which never increases the number of independent sets.<\/jats:p>","DOI":"10.1002\/jgt.22733","type":"journal-article","created":{"date-parts":[[2021,8,11]],"date-time":"2021-08-11T06:55:36Z","timestamp":1628664936000},"page":"175-185","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Maximizing the number of independent sets of fixed size in Kn\u2010covered graphs"],"prefix":"10.1002","volume":"99","author":[{"given":"Anyao","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences University of Science and Technology of China Hefei Anhui China"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-7634-0250","authenticated-orcid":false,"given":"Xinmin","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences University of Science and Technology of China Hefei Anhui China"},{"name":"CAS Key Laboratory of Wu Wen\u2010Tsun Mathematics University of Science and Technology of China Hefei Anhui China"}]},{"given":"Boyuan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences University of Science and Technology of China Hefei Anhui China"}]},{"given":"Yue","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences University of Science and Technology of China Hefei Anhui China"}]}],"member":"311","published-online":{"date-parts":[[2021,8,10]]},"reference":[{"key":"e_1_2_5_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/19M1286712"},{"key":"e_1_2_5_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.22016"},{"key":"e_1_2_5_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21756"},{"key":"e_1_2_5_5_1","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.2001.2063"},{"key":"e_1_2_5_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.06.015"},{"key":"e_1_2_5_7_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548314000546"},{"key":"e_1_2_5_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2018.12.023"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22733","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/jgt.22733","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22733","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T03:15:43Z","timestamp":1693192543000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.22733"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,10]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["10.1002\/jgt.22733"],"URL":"http:\/\/dx.doi.org\/10.1002\/jgt.22733","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,10]]},"assertion":[{"value":"2021-03-25","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-07-28","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-08-10","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}
