The maximum number of halving lines and the rectilinear crossing number of for

DOI10.1016/j.endm.2008.01.045zbMath1341.05034OpenAlexW1521407576MaRDI QIDQ3503562

Silvia Fernández-Merchant, Bernardo M. Ábrego, Gelasio Salazar, Jesús Leaños

Publication date: 5 June 2008

Published in: Electronic Notes in Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.endm.2008.01.045

zbMATH Keywords

complete graphsrectilinear crossing numberhalving lines

Mathematics Subject Classification ID

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

Related Items

A central approach to bound the number of crossings in a generalized configuration ⋮ The maximum multiplicity of a generator in a reduced word ⋮ The 3-symmetric pseudolinear crossing number of \(K_{36}\) ⋮ How to Draw a Planarization ⋮ On \(\leq k\)-edges, crossings, and halving lines of geometric drawings of \(K _{n }\) ⋮ How to Draw a Planarization ⋮ New algorithms and bounds for halving pseudolines ⋮ Point sets that minimize \((\leq k)\)-edges, 3-decomposable drawings, and the rectilinear crossing number of \(K_{30}\) ⋮ 3-symmetric and 3-decomposable geometric drawings of \(K_n\)

Cites Work

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• Proof of Grünbaum's conjecture on the stretchability of certain arrangements of pseudolines
• On halving line arrangements
• New lower bounds for the number of \((\leq k)\)-edges and the rectilinear crossing number of \(K_{n}\)
• A lower bound for the rectilinear crossing number
• Research Problems in Discrete Geometry
• Crossing Number Problems