{"paper":{"title":"Hamiltonian Tetrahedralizations with Steiner Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Francisco Escalona, Jorge Urrutia, Ruy Fabila-Monroy","submitted_at":"2012-10-19T17:44:12Z","abstract_excerpt":"Let $S$ be a set of $n$ points in 3-dimensional space. A tetrahedralization $\\mathcal{T}$ of $S$ is a set of interior disjoint tetrahedra with vertices on $S$, not containing points of $S$ in their interior, and such that their union is the convex hull of $S$. Given $\\mathcal{T}$, $D_\\mathcal{T}$ is defined as the graph having as vertex set the tetrahedra of $\\mathcal{T}$, two of which are adjacent if they share a face. We say that $\\mathcal{T}$ is Hamiltonian if $D_\\mathcal{T}$ has a Hamiltonian path. Let $m$ be the number of convex hull vertices of $S$. We prove that by adding at most $\\lflo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5484","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"}