{"paper":{"title":"Polynomial graph invariants from homomorphism numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Goodall, Delia Garijo, Jaroslav Nesetril","submitted_at":"2013-08-19T12:28:56Z","abstract_excerpt":"We give a method of generating strongly polynomial sequences of graphs, i.e., sequences $(H_{\\mathbf{k}})$ indexed by a multivariate parameter $\\mathbf{k}=(k_1,\\ldots, k_h)$ such that, for each fixed graph $G$, there is a multivariate polynomial $p(G;x_1,\\ldots, x_h)$ such that the number of homomorphisms from $G$ to $H_{\\mathbf{k}}$ is given by the evaluation $p(G;k_1,\\ldots, k_h)$. A classical example is the sequence $(K_k)$ of complete graphs, for which ${\\rm hom}(G,K_k)=P(G;k)$ is the evaluation of the chromatic polynomial at $k$. Our construction produces a large family of graph polynomia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3999","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}