{"paper":{"title":"The Crossing Number of Seq-Shellable Drawings of Complete Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Lutz Oettershagen, Petra Mutzel","submitted_at":"2018-03-20T16:40:07Z","abstract_excerpt":"The Harary-Hill conjecture states that for every $n>0$ the complete graph on $n$ vertices $K_n$, the minimum number of crossings over all its possible drawings equals \\begin{align*} H(n) := \\frac{1}{4}\\Big\\lfloor\\frac{n}{2}\\Big\\rfloor\\Big\\lfloor\\frac{n-1}{2}\\Big\\rfloor\\Big\\lfloor\\frac{n-2}{2}\\Big\\rfloor\\Big\\lfloor\\frac{n-3}{2}\\Big\\rfloor\\text{.} \\end{align*} So far, the lower bound of the conjecture could only be verified for arbitrary drawings of $K_n$ with $n\\leq 12$. In recent years, progress has been made in verifying the conjecture for certain classes of drawings, for example $2$-page-boo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07515","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"}