{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:16Z","timestamp":1753893796407,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The independent set reconfiguration problem asks whether one can transform one given independent set of a graph into another, by changing vertices one by one in such a way the intermediate sets remain independent. Extremal problems on independent sets are widely studied: for example, it is well known that an $n$-vertex graph has at most $3^{n\/3}$ maximum independent sets (and this is tight). This paper investigates the asymptotic behavior of maximum possible length of a shortest reconfiguration sequence for independent sets of size $k$ among all $n$-vertex graphs. We give a tight bound for $k=2$. We also provide a subquadratic upper bound (using the hypergraph removal lemma) as well as an almost tight construction for $k=3$. We generalize our results for larger values of $k$ by proving an $n^{2\\lfloor k\/3 \\rfloor}$ lower bound.<\/jats:p>","DOI":"10.37236\/11771","type":"journal-article","created":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T17:13:14Z","timestamp":1690477994000},"source":"Crossref","is-referenced-by-count":1,"title":["Extremal Independent Set Reconfiguration"],"prefix":"10.37236","volume":"30","author":[{"given":"Nicolas","family":"Bousquet","sequence":"first","affiliation":[]},{"given":"Bastien","family":"Durain","sequence":"additional","affiliation":[]},{"family":"Th\u00e9o Pierron","sequence":"additional","affiliation":[]},{"given":"St\u00e9phan","family":"Thomass\u00e9","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2023,7,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i3p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i3p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T17:13:26Z","timestamp":1690478006000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i3p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,28]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/11771","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,7,28]]},"article-number":"P3.8"}}