{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:12Z","timestamp":1753893852927,"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 is $k$-degenerate if every subgraph has minimum degree at most $k$. \u00a0We provide lower bounds on the size of a maximum induced 2-degenerate subgraph in a triangle-free planar graph. \u00a0We denote the size of a maximum induced 2-degenerate subgraph of a graph $G$ by $\\alpha_2(G)$.\u00a0 We prove that if $G$ is a connected triangle-free planar graph with $n$ vertices and $m$ edges, then $\\alpha_2(G) \\geq \\frac{6n - m - 1}{5}$. \u00a0By Euler's Formula, this implies $\\alpha_2(G) \\geq \\frac{4}{5}n$. \u00a0We also prove that if $G$ is a triangle-free planar graph on $n$ vertices with at most $n_3$ vertices of degree at most three, then $\\alpha_2(G) \\geq \\frac{7}{8}n - 18 n_3$.<\/jats:p>","DOI":"10.37236\/7311","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:36:57Z","timestamp":1578652617000},"source":"Crossref","is-referenced-by-count":1,"title":["Induced 2-Degenerate Subgraphs of Triangle-Free Planar Graphs"],"prefix":"10.37236","volume":"25","author":[{"given":"Zden\u011bk","family":"Dvo\u0159\u00e1k","sequence":"first","affiliation":[]},{"given":"Tom","family":"Kelly","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,3,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p62\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p62\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:37:41Z","timestamp":1579217861000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p62"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/7311","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,3,9]]},"article-number":"P1.62"}}