{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T17:31:27Z","timestamp":1762191087729,"version":"build-2065373602"},"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>Confirming a conjecture posed by Caro, it was shown by Chen and Yu that every graph $G$ with $n$ vertices and at most $2n-4$ edges has a stable cutset, which is a stable set of vertices whose removal disconnects the graph. Le and Pfender showed that all graphs with $n$ vertices and $2n-3$ edges without stable cutset arise from recursively gluing together triangles and triangular prisms along an edge or triangle. Le and Pfender's proof (Electron. J. Combin. 20(1) (2013),\u00a0 #P54)\u00a0 contains a gap, which we fill in the present article.<\/jats:p>","DOI":"10.37236\/13629","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T17:13:41Z","timestamp":1762190021000},"source":"Crossref","is-referenced-by-count":0,"title":["Revisiting Extremal Graphs Having No Stable Cutsets"],"prefix":"10.37236","volume":"32","author":[{"given":"Johannes","family":"Rauch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dieter","family":"Rautenbach","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,11,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p25\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p25\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T17:13:42Z","timestamp":1762190022000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i4p25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,3]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/13629","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,3]]},"article-number":"P4.25"}}