{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T08:05:29Z","timestamp":1773993929619,"version":"3.50.1"},"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 $C_{l}$ denote the cycle of length $l$. For $p\\geq2$ and integer $k\\geq1$, we prove that the function $$ \\phi\\left(  k,p,n\\right)  =\\max_G\\left\\{  \\sum_{u\\in V\\left(  G\\right)  } d^{p}\\left(  u\\right)\\right\\} $$ (where the maximum is over graphs $G$ of order $n$ containing no $C_{2k+2}$) satisfies $\\phi\\left(  k,p,n\\right)  =kn^{p}\\left(  1+o\\left(  1\\right) \\right)$. This settles a conjecture of Caro and Yuster. Our proof is based on a new sufficient condition for long paths.<\/jats:p>","DOI":"10.37236\/196","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:25:33Z","timestamp":1578698733000},"source":"Crossref","is-referenced-by-count":15,"title":["Degree Powers in Graphs with a Forbidden Even Cycle"],"prefix":"10.37236","volume":"16","author":[{"given":"Vladimir","family":"Nikiforov","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,8,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r107\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r107\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T21:41:14Z","timestamp":1579297274000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r107"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8,21]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/196","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,8,21]]},"article-number":"R107"}}