{"paper":{"title":"Quasi-randomness of graph balanced cut properties","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Choongbum Lee, Hao Huang","submitted_at":"2010-09-13T06:56:59Z","abstract_excerpt":"Quasi-random graphs can be informally described as graphs whose edge distribution closely resembles that of a truly random graph of the same edge density. Recently, Shapira and Yuster proved the following result on quasi-randomness of graphs. Let $k \\ge 2$ be a fixed integer, $\\alpha_1,...,\\alpha_k$ be positive reals satisfying $\\sum_{i} \\alpha_i = 1$ and $(\\alpha_1,..., \\alpha_k) \\neq (1/k,...,1/k)$, and $G$ be a graph on $n$ vertices. If for every partition of the vertices of $G$ into sets $V_1,..., V_k$ of size $\\alpha_1 n,..., \\alpha_k n$, the number of complete graphs on $k$ vertices whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2307","kind":"arxiv","version":3},"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"}