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Guo, Kang and Zwaneveld recently studied the relationship between the $d$-defective chromatic number of the $(d+1)$-fold (clique) blowup $G\\boxtimes K_{d+1}$ of a graph $G$ and its ordinary chromatic number, and conjectured that $\\chi(G)=\\chi^d(G\\boxtimes K_{d+1})$ for every graph $G$ and $d\\ge 0$. In this note we disprove this conjecture by constructing graphs $G$ of arbitrarily large chroma"},"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":"2504.01548","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-02T09:44:52Z","cross_cats_sorted":[],"title_canon_sha256":"72022be91883526abec6218c57e08d827a0d69133ca7744f16ab4c9f018c465e","abstract_canon_sha256":"21eeb227fffcb888467f48ac029777a7b98e4982606b0c314c27cf731ba353dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:43:17.059531Z","signature_b64":"ujWQ6TGhzhiWk0FeoSIbx9LzeQItqEiW2B+Hys7fac9otN4j5r8aOPVf3PmhY1zitrndkOmcZKEKdvJpDOB6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f5028408f444f337382f0d47032985e3ae82af79e4f611a218f7777ed4f0a19","last_reissued_at":"2026-07-05T10:43:17.059066Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:43:17.059066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Defective coloring of blowups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Raphael Steiner, Sergey Norin","submitted_at":"2025-04-02T09:44:52Z","abstract_excerpt":"Given a graph $G$ and an integer $d\\ge 0$, its $d$-defective chromatic number $\\chi^d(G)$ is the smallest size of a partition of the vertices into parts inducing subgraphs with maximum degree at most $d$. 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