{"paper":{"title":"Graphs with obstacle number greater than one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chris Hartman, Glenn G. Chappell, Gordon I. Williams, Jill R. Faudree, John Gimbel, Leah Wrenn Berman","submitted_at":"2016-06-12T23:19:37Z","abstract_excerpt":"An \\emph{obstacle representation} of a graph $G$ is a straight-line drawing of $G$ in the plane together with a collection of connected subsets of the plane, called \\emph{obstacles}, that block all non-edges of $G$ while not blocking any of the edges of $G$. The \\emph{obstacle number} obs$(G)$ is the minimum number of obstacles required to represent $G$.\n  We study the structure of graphs with obstacle number greater than one. We show that the icosahedron has obstacle number $2$, thus answering a question of Alpert, Koch, \\& Laison asking whether all planar graphs have obstacle number at most "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03782","kind":"arxiv","version":2},"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"}