{"paper":{"title":"The 2-page crossing number of $K_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Bernardo M. Abrego, Gelasio Salazar, Oswin Aichholzer, Pedro Ramos, Silvia Fernandez-Merchant","submitted_at":"2012-06-25T12:57:21Z","abstract_excerpt":"Around 1958, Hill described how to draw the complete graph $K_n$ with [Z(n) :=1/4\\lfloor \\frac{n}{2}\\rfloor \\lfloor \\frac{n-1}{2}\\rfloor \\lfloor \\frac{n-2}{2}% \\rfloor \\lfloor \\frac{n-3}{2}\\rfloor] crossings, and conjectured that the crossing number $\\crg (K_{n})$ of $K_n$ is exactly Z(n). This is also known as Guy's conjecture as he later popularized it. Towards the end of the century, substantially different drawings of $K_{n}$ with Z(n) crossings were found. These drawings are \\emph{2-page book drawings}, that is, drawings where all the vertices are on a line $\\ell$ (the spine) and each edg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5669","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"}