{"paper":{"title":"The generalized Tur\\'an number for K_3 in graphs without suspensions of a path on five vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Doudou Hei, Xinmin Hou, Yue Ma","submitted_at":"2025-09-04T03:26:40Z","abstract_excerpt":"Given graphs $H$ and $F$, the generalized Tur\\'an number $\\ex(n, H, F)$ is defined as\n  the maximum number of copies of $H$ in an $n$-vertex graph that contains no copy of $F$.\n  The suspension $\\widehat{F}$ of a graph $F$ is\n  obtained by adding a new vertex that is adjacent to every vertex of $F$.\n  Mubayi and Mukherjee (2023, DM) conjectured that $\\ex(n, K_3, \\widehat{P_k})=\\left\\lfloor \\frac{k-2}{2}\\right\\rfloor \\cdot \\frac{n^2}{8}+o(n^2)$, where $P_k$ is a\n  path on $k\\ge 4$ vertices. Using the triangle removal\n  lemma, they verified this conjecture for $k=4,5,6$.\n  Later, Mukherjee (2024"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.03851","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/2509.03851/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"}