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Extremal examples which show optimality of the bound on $\\delta(G)$ are very structured and, in particular, contain large independent sets. In analogy to the Ramsey-Tur\\'an theory, Balogh, Molla, and Sharifzadeh initiated the study of how the absence of such large independent sets influences sufficient minimum degree. We show the following two related results:\n  $\\bullet$ For"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1806.03530","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2018-06-09T19:04:15Z","cross_cats_sorted":[],"title_canon_sha256":"98b10971c86c3986a0973d23950695ce72bfffed6ba496d006bcdd8c602e2b29","abstract_canon_sha256":"e129bda69c57734592edcafe715fea6ed65359b71ec6d652c01fb40be027f0ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:52.154629Z","signature_b64":"eQ0iRzgvsKQ3M1BvfrnGkhoXC1ZlkmOJS7OVnfMwpAD5nnVBuIL40eUry/4YF3+Eeo2eD1kvnTPb4xDlZFKTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"508a424dafaf7179ce5055a398de62bd09ec1343425dc365abdda51b874d54d3","last_reissued_at":"2026-05-18T00:12:52.154086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:52.154086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a Ramsey-Tur\\'an variant of the Hajnal-Szemer\\'edi theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rajko Nenadov, Yanitsa Pehova","submitted_at":"2018-06-09T19:04:15Z","abstract_excerpt":"A seminal result of Hajnal and Szemer\\'{e}di states that if a graph $G$ with $n$ vertices has minimum degree $\\delta(G) \\ge (r-1)n/r$ for some integer $r \\ge 2$, then $G$ contains a $K_r$-factor, assuming $r$ divides $n$. Extremal examples which show optimality of the bound on $\\delta(G)$ are very structured and, in particular, contain large independent sets. In analogy to the Ramsey-Tur\\'an theory, Balogh, Molla, and Sharifzadeh initiated the study of how the absence of such large independent sets influences sufficient minimum degree. 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