{"paper":{"title":"Planar Tur\\'an Number of Double Stars","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Addisu Paulos, Chuanqi Xiao, Debarun Ghosh, Ervin Gy\\H{o}ri","submitted_at":"2021-10-20T11:59:50Z","abstract_excerpt":"Given a graph $F$, the planar Tur\\'an number of $F$, denoted $\\text{ex}_{\\mathcal{P}}(n, F)$, is the maximum number of edges in an $n$-vertex $F$-free planar graph. Such an extremal graph problem was initiated by Dowden while determining sharp upper bound for $\\text{ex}_{\\mathcal{P}}(n,C_4)$ and $\\text{ex}_{\\mathcal{P}}(n,C_5)$, where $C_4$ and $C_5$ are cycles of length four and five respectively. In this paper we determined an upper bound for $\\text{ex}_{\\mathcal{P}}(n,S_{2,2})$, $\\text{ex}_{\\mathcal{P}}(n,S_{2,3})$, $\\text{ex}_{\\mathcal{P}}(n,S_{2,4})$, $\\text{ex}_{\\mathcal{P}}(n,S_{2,5})$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.10515","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/2110.10515/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"}