{"paper":{"title":"Bipartite Tur\\'an problems via graph gluing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hong Liu, Jun Gao, Zichao Dong","submitted_at":"2025-01-22T15:25:14Z","abstract_excerpt":"For graphs $H_1$ and $H_2$, if we glue them by identifying a given pair of vertices $u \\in V(H_1)$ and $v \\in V(H_2)$, what is the extremal number of the resulting graph $H_1^u \\odot H_2^v$? In this paper, we study this problem and show that interestingly it is equivalent to an old question of Erd\\H{o}s and Simonovits on the Zarankiewicz problem. When $H_1, H_2$ are copies of a same bipartite graph $H$ and $u, v$ come from a same part, we prove that $\\operatorname{ex}(n, H_1^u \\odot H_2^v) = \\Theta \\bigl( \\operatorname{ex}(n, H) \\bigr)$. As a corollary, we provide a short self-contained dispro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.12953","kind":"arxiv","version":3},"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/2501.12953/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"}