{"paper":{"title":"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, Patrick Morris, Yoshiharu Kohayakawa, Yury Person","submitted_at":"2018-06-05T13:22:11Z","abstract_excerpt":"We prove that for any $t\\ge 3$ there exist constants $c>0$ and $n_0$ such that any $d$-regular $n$-vertex graph $G$ with $t\\mid n\\geq n_0$ and second largest eigenvalue in absolute value $\\lambda$ satisfying $\\lambda\\le c d^{t}/n^{t-1}$ contains a $K_t$-factor, that is, vertex-disjoint copies of $K_t$ covering every vertex of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01676","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"}