{"paper":{"title":"Extremal graphs for the suspension of edge-critical graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Heng Li, Jianfeng Hou, Qinghou Zeng","submitted_at":"2022-11-15T05:34:46Z","abstract_excerpt":"The Tur\\'{a}n number of a graph $H$, $\\text{ex}(n,H)$, is the maximum number of edges in an $n$-vertex graph that does not contain $H$ as a subgraph. For a vertex $v$ and a multi-set $\\mathcal{F}$ of graphs, the suspension $\\mathcal{F}+v$ of $\\mathcal{F}$ is the graph obtained by connecting the vertex $v$ to all vertices of $F$ for each $F\\in \\mathcal{F}$. For two integers $k\\ge1$ and $r\\ge2$, let $H_i$ be a graph containing a critical edge with chromatic number $r$ for any $i\\in\\{1,\\ldots,k\\}$, and let $H=\\{H_1,\\ldots,H_k\\}+v$. In this paper, we determine $\\text{ex}(n, H)$ and characterize al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07913","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/2211.07913/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"}