{"paper":{"title":"Improved Bounds for the Flat Wall Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Julia Chuzhoy","submitted_at":"2014-10-01T16:29:21Z","abstract_excerpt":"The Flat Wall Theorem of Robertson and Seymour states that there is some function $f$, such that for all integers $w,t>1$, every graph $G$ containing a wall of size $f(w,t)$, must contain either (i) a $K_t$-minor; or (ii) a small subset $A\\subset V(G)$ of vertices, and a flat wall of size $w$ in $G\\setminus A$. Kawarabayashi, Thomas and Wollan recently showed a self-contained proof of this theorem with the following two sets of parameters: (1) $f(w,t)=\\Theta(t^{24}(t^2+w))$ with $|A|=O(t^{24})$, and (2) $f(w,t)=w^{2^{\\Theta(t^{24})}}$ with $|A|\\leq t-5$. The latter result gives the best possib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0276","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":""},"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"}