{"paper":{"title":"Generalized Gray codes with prescribed ends of small dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Tom\\'a\\v{s} Dvo\\v{r}\\'ak, V\\'aclav Koubek","submitted_at":"2017-01-24T01:50:31Z","abstract_excerpt":"Given pairwise distinct vertices $\\{\\alpha_i , \\beta_i\\}^k_{i=1}$ of the $n$-dimensional hypercube $Q_n$ such that the distance of $\\alpha_i$ and $\\beta_i$ is odd, are there paths $P_i$ between $\\alpha_i$ and $\\beta_i$ such that $\\{V (P_i)\\}^k_{i=1}$ partitions $V(Q_n)$? A positive solution for every $n\\ge1$ and $k=1$ is known as a Gray code of dimension $n$. In this paper we settle this problem for small values of $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06705","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"}