{"paper":{"title":"A survey of Zarankiewicz problems in geometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","cs.DM","math.CO"],"primary_cat":"math.HO","authors_text":"Shakhar Smorodinsky","submitted_at":"2024-09-24T13:45:27Z","abstract_excerpt":"One of the central topics in extremal graph theory is the study of the function $ex(n,H)$, which represents the maximum number of edges a graph with $n$ vertices can have while avoiding a fixed graph $H$ as a subgraph. Tur{\\'a}n provided a complete characterization for the case when $H$ is a complete graph on $r$ vertices. Erd{\\H o}s, Stone, and Simonovits extended Tur{\\'a}n's result to arbitrary graphs $H$ with $\\chi(H) > 2$ (chromatic number greater than 2). However, determining the asymptotics of $ex(n, H)$ for bipartite graphs $H$ remains a widely open problem. A classical example of this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.03702","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.03702/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}