{
  "id": "math/0401398",
  "version": "v1",
  "published": "2004-01-28T16:15:25.000Z",
  "updated": "2004-01-28T16:15:25.000Z",
  "title": "A Turán Type Problem Concerning the Powers of the Degrees of a Graph (revised)",
  "authors": [
    "Y. Caro",
    "R. Yuster"
  ],
  "comment": "14 Pages",
  "journal": "The Electronic Journal of Combinatorics 7 (2000), #R47",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a graph $G$ whose degree sequence is $d_{1},..., d_{n}$, and for a positive integer $p$, let $e_{p}(G)=\\sum_{i=1}^{n}d_{i}^{p}$. For a fixed graph $H$, let $t_{p}(n,H)$ denote the maximum value of $e_{p}(G)$ taken over all graphs with $n$ vertices that do not contain $H$ as a subgraph. Clearly, $t_{1}(n,H)$ is twice the Tur\\'{a}n number of $H$. In this paper we consider the case $p>1$. For some graphs $H$ we obtain exact results, for some others we can obtain asymptotically tight upper and lower bounds, and many interesting cases remain open.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-01-28T16:15:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C07"
    ],
    "keywords": [
      "turán type problem concerning",
      "interesting cases remain open",
      "maximum value",
      "exact results",
      "asymptotically tight upper"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......1398C"
    }
  }
}