{"paper":{"title":"Packing 1-Plane Hamiltonian Cycles in Complete Geometric Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hazim Michman Trao","submitted_at":"2016-11-28T12:39:01Z","abstract_excerpt":"Counting the number of Hamiltonian cycles that are contained in a geometric graph is {\\bf \\#P}-complete even if the graph is known to be planar \\cite{lot:refer}. A relaxation for problems in plane geometric graphs is to allow the geometric graphs to be 1-plane, that is, each of its edges is crossed at most once. We consider the following question: For any set $P\\/$ of $n\\/$ points in the plane, how many 1-plane Hamiltonian cycles can be packed into a complete geometric graph $K_n\\/$? We investigate the problem by taking two different situations of $P\\/$, namely, when $P\\/$ is in convex positio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09096","kind":"arxiv","version":4},"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"}