{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T22:01:42Z","timestamp":1761861702379,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A graph $G$ is called $(H;k)$-vertex stable if $G$ contains a subgraph isomorphic to $H$ ever after removing any $k$ of its  vertices; stab$(H;k)$ denotes the minimum size among the sizes of all $(H;k)$-vertex stable graphs. In this paper we deal with $(C_{n};k)$-vertex stable graphs with minimum size. For each $n$ we prove that stab$(C_{n};1)$ is one of only two possible values and we give the exact value for infinitely many $n$'s. Furthermore we establish an upper and lower bound for stab$(C_{n};k)$ for $k\\geq 2$.<\/jats:p>","DOI":"10.37236\/692","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:40:56Z","timestamp":1578696056000},"source":"Crossref","is-referenced-by-count":6,"title":["On $(C_n;k)$ Stable Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"Sylwia","family":"Cichacz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Agnieszka","family":"G\u00f6rlich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Magorzata","family":"Zwonek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrzej","family":"\u017bak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,10,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p205\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p205\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:00:48Z","timestamp":1579284048000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p205"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,17]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/692","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,10,17]]},"article-number":"P205"}}