{"paper":{"title":"On the Euclidean dimension of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Dan Ismailescu, Jin Hyup Hong","submitted_at":"2014-12-31T20:40:31Z","abstract_excerpt":"The Euclidean dimension a graph $G$ is defined to be the smallest integer $d$ such that the vertices of $G$ can be located in $\\mathbb{R}^d$ in such a way that two vertices are unit distance apart if and only if they are adjacent in $G$. In this paper we determine the Euclidean dimension for twelve well known graphs. Five of these graphs, D\\\"{u}rer, Franklin, Desargues, Heawood and Tietze can be embedded in the plane, while the remaining graphs, Chv\\'{a}tal, Goldner-Harrary, Herschel, Fritsch, Gr\\\"{o}tzsch, Hoffman and Soifer have Euclidean dimension $3$. We also present explicit embeddings fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00204","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"}