{"paper":{"title":"Bandwidth theorem for random graphs","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Choongbum Lee, Hao Huang","submitted_at":"2010-05-11T20:41:47Z","abstract_excerpt":"A graph $G$ is said to have \\textit{bandwidth} at most $b$, if there exists a labeling of the vertices by $1,2,..., n$, so that $|i - j| \\leq b$ whenever $\\{i,j\\}$ is an edge of $G$. Recently, B\\\"{o}ttcher, Schacht, and Taraz verified a conjecture of Bollob\\'{a}s and Koml\\'{o}s which says that for every positive $r,\\Delta,\\gamma$, there exists $\\beta$ such that if $H$ is an $n$-vertex $r$-chromatic graph with maximum degree at most $\\Delta$ which has bandwidth at most $\\beta n$, then any graph $G$ on $n$ vertices with minimum degree at least $(1 - 1/r + \\gamma)n$ contains a copy of $H$ for lar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1947","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"}