More on the crossing number of Kn: Monotone drawings

Bernardo M. Ábrego*, Oswin Aichholzer, Silvia Fernández-Merchant, Pedro Ramos, Gelasio Salazar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The Harary-Hill conjecture states that the minimum number of crossings in a drawing of the complete graph Kn is Z(n):=14⌊n2⌋⌊n-12⌋⌊n-22⌋⌊n-32⌋. This conjecture was recently proved for 2-page book drawings of Kn. As an extension of this technique, we prove the conjecture for monotone drawings of Kn, that is, drawings where all vertices have different x-coordinates and the edges are x-monotone curves.

Original languageEnglish
Pages (from-to)411-414
Number of pages4
JournalElectronic Notes in Discrete Mathematics
Publication statusPublished - 5 Nov 2013


  • Complete graph
  • Crossing number
  • K-edge
  • Monotone drawing
  • Topological drawing

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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