{"paper":{"title":"Weighted Turan Problems with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maria Talanda-Fisher, Patrick Bennett, Sean English","submitted_at":"2018-09-13T16:03:03Z","abstract_excerpt":"Suppose the edges of $K_n$ are assigned weights by a weight function $w$. We define the {\\em weighted extremal number}\n  \\[\n  \\mathrm{ex}(n,w,F):=\\max\\{w(G)\\mid G\\subseteq K_n,\\text{ and }G\\text{ is }F\\text{-free}\\}\n  \\]\n  where $w(G):=\\sum_{e\\in E(G)}w(e)$. In this paper we study this problem for two types of weights $w$, each of which has an application. The first application is to an extremal problem in a complete multipartite host graph. The second application is to the maximum rectilinear crossing number of trees of diameter 4."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05028","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"}