## Abstract

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

Original language | English |
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Pages (from-to) | 411-414 |

Number of pages | 4 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 44 |

DOIs | |

Publication status | Published - 5 Nov 2013 |

## Keywords

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

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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