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If $G$ is a tripartite graph with $N$ vertices in each vertex class such that every vertex is adjacent to at least $2N/3+2h-1$ vertices in each of the other classes, then $G$ can be tiled perfectly by copies of $K_{h,h,h}$. This extends work by two of the authors [Electron. J. Combin, 16(1), 2009] and also gives a sufficient condition for tiling by any fixed 3-colorable graph. Furthermore, we show that $2N/3+2h-1$ in our result can not be replaced by $2N/3+ h-2$ and that if $N$ is divisible by $6h$, then we can rep"},"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":"1001.1002","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-01-06T22:18:39Z","cross_cats_sorted":[],"title_canon_sha256":"5e0b43503b6ce6ed22596a22c5ea629f372ee6e588e022ec145272a3163a00a0","abstract_canon_sha256":"ed91ce5e1df3ac58898906b33ccc0141e370b241ecfa6f2f6e171307623292e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:24.481356Z","signature_b64":"/v8/ZJ776jal78RyjxG4d8vt8/djE1f6eMzAMMQwcVT/LzjSR/R15k6KvI2oCOKBLhoPV4A+P1umuW7tydUFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d69d8ccd09ab75508b5ae1e7456be7b6a39392bad4f9473b92dc38f36f613bb0","last_reissued_at":"2026-05-18T00:08:24.480154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:24.480154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tiling tripartite graphs with 3-colorable graphs: The extreme case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kirsten Hogenson, Ryan R. 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