{"paper":{"title":"Degree powers in $C_5$-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ran Gu, Xueliang Li, Yongtang Shi","submitted_at":"2013-04-05T11:12:14Z","abstract_excerpt":"Let $G$ be a graph with degree sequence $d_1,d_2,\\ldots,d_n$. Given a positive integer $p$, denote by $e_p(G)=\\sum_{i=1}^n d_i^p$. Caro and Yuster introduced a Tur\\'an-type problem for $e_p(G)$: given an integer $p$, how large can $e_p(G)$ be if $G$ has no subgraph of a particular type. They got some results for the subgraph of particular type to be a clique of order $r+1$ and a cycle of even length, respectively. Denote by $ex_p(n,H)$ the maximum value of $e_p(G)$ taken over all graphs with $n$ vertices that do not contain $H$ as a subgraph. Clearly, $ex_1(n,H)=2ex(n,H)$, where $ex(n,H)$ deno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1680","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}