An ongoing project to improve the rectilinear and the pseudolinear crossing constants

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...

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Detalles Bibliográficos
Autores: Oswin Aichholzer, Frank Duque, RUY FABILA MONROY, OSCAR EDUARDO GARCIA QUINTERO, Carlos Hidalgo_Toscano
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:México
Institución:Centro de Investigación e Innovación en Tecnologías de la Información y Comunicación
Repositorio:Repositorio Institucional de INFOTEC
Idioma:inglés
OAI Identifier:oai:infotec.repositorioinstitucional.mx:1027/435
Acceso en línea:http://infotec.repositorioinstitucional.mx/jspui/handle/1027/435
Access Level:acceso abierto
Palabra clave:info:eu-repo/classification/Tesauro de la UNESCO/Algorithms
info:eu-repo/classification/Tesauro de la UNESCO/Graphs
info:eu-repo/classification/Tesauro de la UNESCO/Mathematics and statistics
info:eu-repo/classification/cti/1
info:eu-repo/classification/cti/12
info:eu-repo/classification/cti/1299
Descripción
Sumario: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 Kn.