{"paper":{"title":"Degree powers in graphs with a forbidden forest","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henry Liu, Yongtang Shi, Yongxin Lan, Zhongmei Qin","submitted_at":"2018-01-06T14:43:01Z","abstract_excerpt":"Given a positive integer $p$ and a graph $G$ with degree sequence $d_1,\\dots,d_n$, we define $e_p(G)=\\sum_{i=1}^n d_i^p$. Caro and Yuster introduced a Tur\\'an-type problem for $e_p(G)$: Given a positive integer $p$ and a graph $H$, determine the function $ex_p(n,H)$, which is the maximum value of $e_p(G)$ taken over all graphs $G$ on $n$ vertices that do not contain $H$ as a subgraph. Clearly, $ex_1(n,H)=2ex(n,H)$, where $ex(n,H)$ denotes the classical Tur\\'an number. Caro and Yuster determined the function $ex_p(n, P_\\ell)$ for sufficiently large $n$, where $p\\geq 2$ and $P_\\ell$ denotes the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02023","kind":"arxiv","version":1},"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"}