{"paper":{"title":"Interdependencies of less-equal-relations between partial Lov\\'{a}sz-vectors of digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Frank a Campo","submitted_at":"2020-04-24T11:08:45Z","abstract_excerpt":"For digraphs $G$ and $H$, let ${\\cal H}(G,H)$ be the set of all homomorphisms from $G$ to $H$, and let ${\\cal S}(G,H)$ be the subset of those homomorphisms mapping all proper arcs in $G$ to proper arcs in $H$. From an earlier investigation we know that for certain digraphs $R$ and $S$, the relation \"$\\# {\\cal S}(G,R) \\leq \\# {\\cal S}(G,S)$ for all $G \\in \\mathfrak{ D }'$\" implies \"$\\# {\\cal H}(G,R) \\leq \\# {\\cal H}(G,S)$ for all $G \\in \\mathfrak{ D }'$\", where $\\mathfrak{ D }'$ is a subclass of digraphs. Now we ask for the inverse: For which digraphs $R, S$ and which subclasses $\\mathfrak{ D }"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.11653","kind":"arxiv","version":3},"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/2004.11653/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"}