{"paper":{"title":"Polynomial expansion and sublinear separators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jean-Florent Raymond, Louis Esperet","submitted_at":"2017-05-03T14:12:45Z","abstract_excerpt":"Let $\\mathcal{C}$ be a class of graphs that is closed under taking subgraphs. We prove that if for some fixed $0<\\delta\\le 1$, every $n$-vertex graph of $\\mathcal{C}$ has a balanced separator of order $O(n^{1-\\delta})$, then any depth-$k$ minor (i.e. minor obtained by contracting disjoint subgraphs of radius at most $k$) of a graph in $\\mathcal{C}$ has average degree $O\\big((k \\text{ polylog }k)^{1/\\delta}\\big)$. This confirms a conjecture of Dvo\\v{r}\\'ak and Norin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01438","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"}