Geodesic
An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants
Journal of graph algorithms and applications, Tome 24 (2020) no. 3, pp. 421-432 Cet article a éte moissonné depuis la source Journal of Graph Algorythms and Applications website

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A drawing of a graph in the plane is pseudolinear if the edges of the drawing can be extended to doubly-infinite curves that form an arrangement of pseudolines, that is, any pair of these curves crosses precisely once. A special case is rectilinear drawings where the edges of the graph are drawn as straight line segments. The rectilinear (pseudolinear) crossing number of a graph is the minimum number of pairs of edges of the graph that cross in any of its rectilinear (pseudolinear) drawings. In this paper we describe an ongoing project to continuously obtain better asymptotic upper bounds on the rectilinear and pseudolinear crossing number of the complete graph $K_n$.
DOI : 10.7155/jgaa.00540
Keywords: rectilinear crossing number, pseudolinear crossing number, crossing minimization, graph drawing 
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     author = {Oswin Aichholzer and Frank Duque and Ruy Fabila-Monroy and Oscar Garc{\'\i}a-Quintero and Carlos Hidalgo-Toscano},
     title = {An {Ongoing} {Project} to {Improve} the {Rectilinear} and the {Pseudolinear} {Crossing} {Constants}},
     journal = {Journal of graph algorithms and applications},
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Oswin Aichholzer; Frank Duque; Ruy Fabila-Monroy; Oscar García-Quintero; Carlos Hidalgo-Toscano. An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants. Journal of graph algorithms and applications, Tome 24 (2020) no. 3, pp. 421-432. doi: 10.7155/jgaa.00540

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