{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:41Z","timestamp":1753893821900,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We show that every graph $G$ of maximum degree $\\Delta$ and sufficiently large order has a vertex cutset $S$ of order at most $\\Delta$ that induces a subgraph $G[S]$ of maximum degree at most $\\Delta-3$. For $\\Delta\\in \\{ 4,5\\}$, we refine this result by considering also\u00a0the average degree of $G[S]$. If $G$ has no $K_{r,r}$ subgraph, then we show the existence of a vertex cutset that induces a subgraph of maximum degree at most $\\Big(1-\\frac{1}{{r\\choose 2}}\\Big)\\Delta+O(1)$.<\/jats:p>","DOI":"10.37236\/12902","type":"journal-article","created":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T14:33:08Z","timestamp":1747924388000},"source":"Crossref","is-referenced-by-count":0,"title":["Sparse Vertex Cutsets and the Maximum Degree"],"prefix":"10.37236","volume":"32","author":[{"given":"St\u00e9phane","family":"Bessy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Johannes","family":"Rauch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dieter","family":"Rautenbach","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"U\u00e9verton S.","family":"Souza","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,5,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p32\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T14:33:08Z","timestamp":1747924388000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i2p32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,23]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,4,11]]}},"URL":"https:\/\/doi.org\/10.37236\/12902","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2025,5,23]]},"article-number":"P2.32"}}