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Filtering by: Subject Rectilinear crossing number Remove constraint Subject: Rectilinear crossing number

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  • Work
    Article
    Leanos, Jesus
    Recently, Aichholzer, García, Orden, and Ramos derived a remarkably improved lower bound for the number of (⩽k)-edges in an n-point set, and as an immediate corollary, an improved lower bound on the rectilinear crossing number of Kn. We use simple all . . .
  • Work
    Article
    Fernandez, Silvia
    We give a new upper bound for the rectilinear crossing number of the complete geometric graph . We prove that by means of a new construction based on an iterative duplication strategy starting with a set having a certain structure of halving lines.
  • Work
    Article
    Fernandez, Silvia
    The of a drawing of a graph is the largest number of crossings on any edge of the drawing. In a of a graph, the vertices are points in the plane in general position and the edges are straight-line segments. The of the complete graph , denoted by , is . . .
  • Work
    Article
    Abrego, Bernardo
    We show that, up to isomorphism, there is a unique crossing-minimal rectilinear drawing of K18. As a consequence we settle, in the negative, the following question from Aichholzer and Krasser: does there always exist an crossing-minimal drawing of Kn . . .