{"paper":{"title":"(Injective) hom-complexity between graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cesar A. Ipanaque Zapata, Josu\\'e A. Aguirre Enciso, Wilman Francisco Cuba Ramos","submitted_at":"2024-11-25T16:31:17Z","abstract_excerpt":"We present the notion of hom-complexity, $\\text{C}(G;H)$, for two graphs $G$ and $H$, along with basic results for this numerical invariant. This invariant $\\text{C}(G;H)$ is a number that measures the \\aspas{complexity} of the question: when is there a homomorphism $G\\to H$? More precisely, $\\text{C}(G;H)$ is the least positive integer $k$ such that there are $k$ different subgraphs $G_j$ of $G$ such that $G=G_1\\cup\\cdots\\cup G_k$, and for each $G_j$, there is a homomorphism $G_j\\to H$. Likewise, we introduce the notion of injective hom-complexity, $\\text{IC}(G;H)$. The (injective) hom-comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16547","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/2411.16547/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"}