{"paper":{"title":"Near-perfect clique-factors in sparse pseudorandom graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Han, Yoshiharu Kohayakawa, Yury Person","submitted_at":"2018-06-01T18:09:19Z","abstract_excerpt":"We prove that, for any $t\\ge 3$, there exists a constant $c=c(t)>0$ such that any $d$-regular $n$-vertex graph with the second largest eigenvalue in absolute value~$\\lambda$ satisfying $\\lambda\\le c d^{t-1}/n^{t-2}$ contains vertex-disjoint copies of $K_t$ covering all but at most $n^{1-1/(8t^4)}$ vertices. This provides further support for the conjecture of Krivelevich, Sudakov and Sz\\'abo [\\emph{Triangle factors in sparse pseudo-random graphs}, Combinatorica \\textbf{24} (2004), pp.~403--426] that $(n,d,\\lambda)$-graphs with $n\\in 3\\mathbb{N}$ and $\\lambda\\leq cd^{2}/n$ for a suitably small a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00493","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"}