{"paper":{"title":"Hamiltonian Cycle in Semi-Equivelar Maps on the Torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Ashish Kumar Upadhyay, Dipendu Maity","submitted_at":"2013-08-30T11:58:45Z","abstract_excerpt":"Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. There are eight semi-equivelar maps of types $\\{3^{3},4^{2}\\}$, $\\{3^{2},4,3,4\\}$, $\\{6,3,6,3\\}$, $\\{3^{4},6\\}$, $\\{4,8^{2}\\}$, $\\{3,12^{2}\\}$, $\\{4,6,12\\}$, $\\{6,4,3,4\\}$ exist on the torus. In this article we show the existence of Hamiltonian cycle in each semi-equivelar map on the torus except the map of type $\\{3,12^{2}\\}$. This result gives the partial solution to the conjecture which is given by Gr$\\ddot{u}$nbaum \\cite{grunbaum} and Nash-Williams \\cite{nash williams} that every 4-connected "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6717","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"}