{"paper":{"title":"Drawing graphs using a small number of obstacles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Josef Cibulka, Martin Balko, Pavel Valtr","submitted_at":"2016-10-15T14:19:29Z","abstract_excerpt":"An obstacle representation of a graph $G$ is a set of points in the plane representing the vertices of $G$, together with a set of polygonal obstacles such that two vertices of $G$ are connected by an edge in $G$ if and only if the line segment between the corresponding points avoids all the obstacles. The obstacle number ${\\rm obs}(G)$ of $G$ is the minimum number of obstacles in an obstacle representation of $G$.\n  We provide the first non-trivial general upper bound on the obstacle number of graphs by showing that every $n$-vertex graph $G$ satisfies ${\\rm obs}(G) \\leq n\\lceil\\log{n}\\rceil-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04741","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"}