Geometric drawings of \(K_{n}\) with few crossings

DOI10.1016/j.jcta.2006.05.003zbMath1115.05018OpenAlexW1959454134MaRDI QIDQ868888

Silvia Fernández-Merchant, Bernardo M. Ábrego

Publication date: 26 February 2007

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2006.05.003

zbMATH Keywords

rectilinear crossing numbergeometric graphcomplete graphconvex quadrilateral

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (10)

The rectilinear local crossing number of \(K_{n}\) ⋮ A lower bound on the crossing number of uniform hypergraphs ⋮ The maximum number of halving lines and the rectilinear crossing number of for ⋮ A central approach to bound the number of crossings in a generalized configuration ⋮ The 3-symmetric pseudolinear crossing number of \(K_{36}\) ⋮ An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants ⋮ On the 2-colored crossing number ⋮ On \(\leq k\)-edges, crossings, and halving lines of geometric drawings of \(K _{n }\) ⋮ Simultaneous Embeddings with Few Bends and Crossings ⋮ 3-symmetric and 3-decomposable geometric drawings of \(K_n\)

Cites Work

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• On the crossing number of complete graphs
• Toward the rectilinear crossing number of \(K _{n}\): New drawings, upper bounds, and asymptotics
• \(k\)-sets, convex quadrilaterals, and the rectilinear crossing number of \(K_{n}\)
• An upper bound for the rectilinear crossing number of the complete graph
• A lower bound for the rectilinear crossing number
• The Rectilinear Crossing Number of a Complete Graph and Sylvester's "Four Point Problem" of Geometric Probability
• Abstract order type extension and new results on the rectilinear crossing number

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