{"paper":{"title":"Extremal number of edges in graphs without homeomorphically irreducible spanning trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huiqing Liu, Xiaolan Hu, Yibo Li","submitted_at":"2026-06-10T13:52:21Z","abstract_excerpt":"For integers $k\\ge 1$ and $n\\ge k+1$, let $\\operatorname{ex}^{\\mathrm{HIST}}_k(n)$ denote the maximum number of edges in a $k$-connected graph of order $n$ which contains no homeomorphically irreducible spanning tree (or briefly HIST). We determine these extremal numbers for $k=1$ and $k=2$. More precisely, we prove that $\\operatorname{ex}^{\\mathrm{HIST}}_1(n)=\\binom{n-2}{2}+2$ for $n\\ge 9$, with $L_n$ as the unique extremal graph, and that $\\operatorname{ex}^{\\mathrm{HIST}}_2(n)=\\binom{n-3}{2}+4$ for $n\\ge 13$, with $B_n$ as the unique extremal graph. This provides a Tur\\'an-type extremal res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12093","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/2606.12093/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"}