{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:55Z","timestamp":1753893835967,"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>Let $\\Delta_k$ denote the maximum degree of the $k^{\\rm th}$ iterated line graph $L^k(G)$. For any connected graph $G$ that is not a path, the inequality $\\Delta_{k+1}\\leq 2\\Delta_k-2$ holds. Niepel, Knor, and \u0160olt\u00e9s have conjectured that there exists an integer $K$ such that, for all $k\\geq K$, equality holds; that is, the maximum degree $\\Delta_k$ attains the greatest possible growth. We prove this conjecture using induced subgraphs of maximum degree vertices and locally maximum vertices.<\/jats:p>","DOI":"10.37236\/1460","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:00:32Z","timestamp":1578708032000},"source":"Crossref","is-referenced-by-count":7,"title":["Maximum Degree Growth of the Iterated Line Graph"],"prefix":"10.37236","volume":"6","author":[{"given":"Stephen G.","family":"Hartke","sequence":"first","affiliation":[]},{"given":"Aparna W.","family":"Higgins","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1999,6,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:32:56Z","timestamp":1579325576000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v6i1r28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,6,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1999,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1460","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1999,6,24]]},"article-number":"R28"}}