Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 165-01. The crossing number of complete graphs
Manuscript map · lines 5485–5494
OpenAI@2026-10-07#rem:oai-p-165-01
Authors: OpenAI. Family 165.
Title: The crossing number of complete graphs.
Abstract: We prove the Harary–Hill conjecture: for every positive integer n, the ordinary crossing number of the complete graph Kn is ${}displaystyle {}frac14{}left{}lfloor{}frac n2{}right{}rfloor {}left{}lfloor{}frac{n-1}{2}{}right{}rfloor {}left{}lfloor{}frac{n-2}{2}{}right{}rfloor {}left{}lfloor{}frac{n-3}{2}{}right{}rfloor.$
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- section: Manuscript map
- remark: Remark: 001-01. Milne's rationality conjecture for abelian varieties
- remark: Remark: 002-01. Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank
- remark: Remark: 002-02. The Selmer converse for elliptic curves at every prime
- remark: Remark: 002-03. The two-primary Birch–Swinnerton-Dyer formula in Selmer corank at most one
- remark: Remark: 003-01. The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane s 7/8
- remark: Remark: 003-02. The Quasi-Riemann Hypothesis (alternate 11/12 proof)
- remark: Remark: 003-03. Uniform exclusion of Landau–Siegel zeros