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The complexity of exact minimization of this problem is well understood [34], and the class of digraphs H, for which the MinHOM(H) is polynomial time solvable is a small subset of all digraphs.\n  In this paper, we consider the approximation of MinHOM within a constant factor. For digraphs, MinHOM(H) is not approximable if"},"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":"1902.02201","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-06T14:27:25Z","cross_cats_sorted":[],"title_canon_sha256":"4dc47f461cd115fe1c59f9091e39a427c5b0c347c24b6efcc90c6a0eb2bf9f99","abstract_canon_sha256":"b51acdba3e6bbf946be13eee7c31a6243e0f23260ce813f90260b62766d35d2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:17:57.724448Z","signature_b64":"ZD1MTNS3FUkTN/O3BOm35qY5+jIXZ+//L5m/R3wJfAhIh6gTIqeFxUPyXLxCxlfJLjNEG3Ysl06pISKUIqSuCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1de533353d40602bce03417af9993e6c5b317ca2f2ee6912764189e178e9bbe0","last_reissued_at":"2026-07-05T05:17:57.724044Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:17:57.724044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toward a Dichotomy for Approximation of $H$-coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Akbar Rafiey, Arash Rafiey, Thiago Santos","submitted_at":"2019-02-06T14:27:25Z","abstract_excerpt":"Given two (di)graphs G, H and a cost function $c:V(G)\\times V(H) \\to \\mathbb{Q}_{\\geq 0}\\cup\\{+\\infty\\}$, in the minimum cost homomorphism problem, MinHOM(H), goal is finding a homomorphism $f:V(G)\\to V(H)$ (a.k.a H-coloring) that minimizes $\\sum\\limits_{v\\in V(G)}c(v,f(v))$. The complexity of exact minimization of this problem is well understood [34], and the class of digraphs H, for which the MinHOM(H) is polynomial time solvable is a small subset of all digraphs.\n  In this paper, we consider the approximation of MinHOM within a constant factor. 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