{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T21:09:53Z","timestamp":1779397793370,"version":"3.53.1"},"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>Given a graph $G$ and a non-negative integer $d$ let $\\alpha_d(G)$ be the order of a largest induced $d$-degenerate subgraph of $G$. We prove that for any pair of non-negative integers $k&gt;d$, if $G$ is a $k$-degenerate graph, then $\\alpha_d(G) \\geq \\max\\{ \\frac{(d+1)n}{k+d+1}, n - \\alpha_{k-d-1}(G)\\}$. For $k$-degenerate graphs this improves a more general lower bound of Alon, Kahn, and Seymour. By modifying our arguments we also obtain an improved lower bounds on $\\alpha_d(G)$ for graphs of bounded genus. This extends earlier work on degenerate subgraphs of planar graphs.<\/jats:p>","DOI":"10.37236\/14959","type":"journal-article","created":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T20:51:20Z","timestamp":1779396680000},"source":"Crossref","is-referenced-by-count":0,"title":["A Note on Large Degenerate Induced Subgraphs in Sparse Graphs"],"prefix":"10.37236","volume":"33","author":[{"given":"Alexander","family":"Clow","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sean","family":"Kim","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ladislav","family":"Stacho","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2026,5,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p41\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p41\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T20:51:20Z","timestamp":1779396680000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i2p41"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,22]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/14959","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,22]]},"article-number":"P2.41"}}