{"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. For digraphs, MinHOM(H) is not approximable if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02201","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1902.02201/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}