{"paper":{"title":"Large Minors in Expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Julia Chuzhoy, Rachit Nimavat","submitted_at":"2019-01-27T10:47:49Z","abstract_excerpt":"In this paper we study expander graphs and their minors. Specifically, we attempt to answer the following question: what is the largest function $f(n,\\alpha,d)$, such that every $n$-vertex $\\alpha$-expander with maximum vertex degree at most $d$ contains {\\bf every} graph $H$ with at most $f(n,\\alpha,d)$ edges and vertices as a minor? Our main result is that there is some universal constant $c$, such that $f(n,\\alpha,d)\\geq \\frac{n}{c\\log n}\\cdot \\left(\\frac{\\alpha}{d}\\right )^c$. This bound achieves a tight dependence on $n$: it is well known that there are bounded-degree $n$-vertex expanders"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09349","kind":"arxiv","version":2},"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"}