{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:16:20Z","timestamp":1759637780998,"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 $k$-degenerate if it can be transformed into an empty graph by\u00a0subsequent removals of vertices of degree $k$ or less. We prove that every connected\u00a0planar graph with average degree $d \\ge \u00a02$ has a $4$-degenerate induced subgraph containing\u00a0at least $ (38 - d)\/36$ of its vertices. This shows that every planar graph of\u00a0order $n$ has a $4$-degenerate induced subgraph of order more than $8\/9 \\cdot n$. We also\u00a0consider a local variation of this problem and show that in every planar graph with\u00a0at least 7 vertices, deleting a suitable vertex allows us to subsequently remove at\u00a0least 6 more vertices of degree four or less.<\/jats:p>","DOI":"10.37236\/4265","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:33:09Z","timestamp":1578702789000},"source":"Crossref","is-referenced-by-count":2,"title":["Maximum 4-Degenerate Subgraph of a Planar Graph"],"prefix":"10.37236","volume":"22","author":[{"given":"Robert","family":"Lukot'ka","sequence":"first","affiliation":[]},{"given":"J\u00e1n","family":"Maz\u00e1k","sequence":"additional","affiliation":[]},{"given":"Xuding","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,1,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:38:34Z","timestamp":1579257514000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4265","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,1,20]]},"article-number":"P1.11"}}