{"paper":{"title":"Tur\\'an problems for suspension of a balanced tree","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fangfang Zhang, Xiaolin Wang, Xiutao Zhu, Yanbo Zhang","submitted_at":"2025-03-07T06:11:04Z","abstract_excerpt":"The Tur\\'an number $\\ex(n,H)$ is the maximum number of edges that an $n$-vertex $H$-free graph can have. The suspension $\\widehat{H}$ is obtained from $H$ by adding a new vertex which is adjacent to all vertices of $H$ and a tree is balanced if the sizes of its two color classes differ at most $1$. In this paper, we obtain a sharp bound of $\\ex(n,\\widehat{T})$ when $n\\ge 4(4k)^6$ based on the Erd\\H{o}s-S\\'os conjecture. We also show the bound is sharp for infinitely many $n$ and characterize all extremal graphs. In particular, if $T$ satisfies some conditions such as $T$ contains a matching co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05166","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.05166/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"}