{"paper":{"title":"The Density Tur\\'an problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"P\\'eter Csikv\\'ari, Zolt\\'an L\\'or\\'ant Nagy","submitted_at":"2014-07-29T20:08:39Z","abstract_excerpt":"Let $H$ be a graph on $n$ vertices and let the blow-up graph\n  $G[H]$ be defined as follows. We replace each vertex $v_i$ of $H$ by a cluster\n  $A_i$ and connect some pairs of vertices of $A_i$ and $A_j$ if $(v_i,v_j)$ was\n  an edge of the graph $H$. As usual, we define the edge density between $A_i$ and $A_j$ as $d(A_i,A_j)=\\frac{e(A_i,A_j)}{|A_i||A_j|}.$ We study the following problem. Given densities $\\gamma_{ij}$ for each edge $(i,j)\\in E(H)$. Then one has to decide whether there exists a blow-up graph $G[H]$ with edge densities at least $\\gamma_{ij}$ such that one cannot choose a vertex f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7873","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"}