{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:07Z","timestamp":1753893847760,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $P_{n}$ be a path graph on $n$ vertices. We say that a graph $G$ is $P_{n}$-induced-saturated if $G$ contains no induced copy of $P_{n}$, but deleting any edge of $G$ as well as adding to $G$ any edge of $G^{c}$ creates such a copy. Martin and Smith (2012) showed that there is no $P_{4}$-induced-saturated graph. On the other hand, there trivially exist $P_{n}$-induced-saturated graphs for $n=2,3$. Axenovich and Csik\u00f3s (2019) ask for which integers $n \\geqslant 5$ do there exist $P_{n}$-induced-saturated graphs. R\u00e4ty (2019) constructed such a graph for $n=6$, and Cho, Choi and Park (2019) later constructed such graphs for all $n=3k$ for $k \\geqslant 2$. We show by a different construction that $P_{n}$-induced-saturated graphs exist for all $n \\geqslant 6$, leaving only the case $n=5$ open.<\/jats:p>","DOI":"10.37236\/9579","type":"journal-article","created":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T08:21:31Z","timestamp":1608020491000},"source":"Crossref","is-referenced-by-count":0,"title":["$P_{n}$-Induced-Saturated Graphs Exist for all $n \\geqslant 6$"],"prefix":"10.37236","volume":"27","author":[{"given":"Vojt\u011bch","family":"Dvo\u0159\u00e1k","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,12,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p43\/8224","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p43\/8224","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T08:21:31Z","timestamp":1608020491000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,11]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/9579","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,12,11]]},"article-number":"P4.43"}}