{"paper":{"title":"On k-visibility graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"J.T. Geneson, Matthew Babbitt, Tanya Khovanova","submitted_at":"2013-05-02T16:43:35Z","abstract_excerpt":"We examine several types of visibility graphs in which sightlines can pass through $k$ objects. For $k \\geq 1$ we bound the maximum thickness of semi-bar $k$-visibility graphs between $\\lceil \\frac{2}{3} (k + 1) \\rceil$ and $2k$. In addition we show that the maximum number of edges in arc and circle $k$-visibility graphs on $n$ vertices is at most $(k+1)(3n-k-2)$ for $n > 4k+4$ and ${n \\choose 2}$ for $n \\leq 4k+4$, while the maximum chromatic number is at most $6k+6$. In semi-arc $k$-visibility graphs on $n$ vertices, we show that the maximum number of edges is ${n \\choose 2}$ for $n \\leq 3k+"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0505","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"}