{"paper":{"title":"On Sets of Lines Not-Supporting Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Daniel Neuwirth, Radoslav Fulek","submitted_at":"2011-04-07T11:56:39Z","abstract_excerpt":"We study the following problem introduced by Dujmovic et al. Given a tree $T = (V,E)$, on $n$ vertices, a set of $n$ lines $\\mathcal{L}$ in the plane and a bijection $\\iota: V \\rightarrow \\mathcal{L}$, we are asked to find a crossing-free straight-line embedding of $T$ so that $v\\in \\iota(v)$, for all $v\\in V$. We say that a set of $n$ lines $\\mathcal{L}$ is universal for trees if for any tree $T$ and any bijection $\\iota$ there exists such an embedding. We prove that any sufficiently big set of lines is not universal for trees, which solves an open problem asked by Dujmovic et al."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1307","kind":"arxiv","version":8},"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"}