{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T08:05:18Z","timestamp":1773993918844,"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>For every real $p&gt;0$ and simple graph $G,$ set $$ f\\left(  p,G\\right)  =\\sum_{u\\in V\\left(  G\\right)  }d^{p}\\left( u\\right)  , $$ and let $\\phi\\left(  r,p,n\\right)  $ be the maximum of $f\\left( p,G\\right)  $ taken over all $K_{r+1}$-free graphs $G$ of order $n.$ We prove that, if $0 &lt; p &lt; r,$ then$$ \\phi\\left(  r,p,n\\right)  =f\\left(  p,T_{r}\\left(  n\\right) \\right)  , $$ where $T_{r}\\left(  n\\right)  $ is the $r$-partite Turan graph of order $n$. For every $p\\geq r+\\left\\lceil \\sqrt{2r}\\right\\rceil $ and $n$ large, we show that$$ \\phi\\left(  p,n,r\\right)  &gt;\\left(  1+\\varepsilon\\right)  f\\left( p,T_{r}\\left(  n\\right)  \\right) $$ for some $\\varepsilon=\\varepsilon\\left(  r\\right)  &gt;0.$ Our results settle two conjectures of Caro and Yuster.<\/jats:p>","DOI":"10.37236\/1795","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:21:12Z","timestamp":1578720072000},"source":"Crossref","is-referenced-by-count":17,"title":["Degree Powers in Graphs with Forbidden Subgraphs"],"prefix":"10.37236","volume":"11","author":[{"given":"B\u00e9la","family":"Bollob\u00e1s","sequence":"first","affiliation":[]},{"given":"Vladimir","family":"Nikiforov","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,6,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r42\/comment","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r42\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:02:14Z","timestamp":1579323734000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,6,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1795","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,6,25]]},"article-number":"R42"}}