{"paper":{"title":"Spanning trees in graphs without large bipartite holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Donglei Yang, Guanghui Wang, Jie Han, Jie Hu, Lidan Ping, Yi Wang","submitted_at":"2023-02-08T09:49:01Z","abstract_excerpt":"We show that for any $\\varepsilon>0$ and $\\Delta\\in\\mathbb{N}$, there exists $\\alpha>0$ such that for sufficiently large $n$, every $n$-vertex graph $G$ satisfying that $\\delta(G)\\geq\\varepsilon n$ and $e(X, Y)>0$ for every pair of disjoint vertex sets $X, Y\\subseteq V(G)$ of size $\\alpha n$ contains all spanning trees with maximum degree at most $\\Delta$. This strengthens a result of B\\\"ottcher et al."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.03966","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/2302.03966/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"}