An extended lower bound on the number of(\(\leqslant k\))-edges to generalized configurations of points and the pseudolinear crossing number of \(K_n\)

DOI10.1016/j.jcta.2007.11.004zbMath1165.05006OpenAlexW2080315833MaRDI QIDQ958731

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

Publication date: 8 December 2008

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.2007.11.004

zbMATH Keywords

complete graphsrectilinear crossing number\(k\)-edgesallowable sequenceshalving lineshalving pseudolinespseudolinear crossing number

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Planar graphs; geometric and topological aspects of graph theory (05C10) Erd?s problems and related topics of discrete geometry (52C10)

Related Items (6)

The 3-symmetric pseudolinear crossing number of \(K_{36}\) ⋮ On \(\leq k\)-edges, crossings, and halving lines of geometric drawings of \(K _{n }\) ⋮ Crossing numbers and combinatorial characterization of monotone drawings of \(K_n\) ⋮ New algorithms and bounds for halving pseudolines ⋮ Point sets that minimize \((\leq k)\)-edges, 3-decomposable drawings, and the rectilinear crossing number of \(K_{30}\) ⋮ Turán’s Brick Factory Problem: The Status of the Conjectures of Zarankiewicz and Hill

Cites Work

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• On the combinatorial classification of nondegenerate configurations in the plane
• On halving line arrangements
• New lower bounds for the number of \((\leq k)\)-edges and the rectilinear crossing number of \(K_{n}\)
• \(k\)-sets, convex quadrilaterals, and the rectilinear crossing number of \(K_{n}\)
• A lower bound for the rectilinear crossing number
• Research Problems in Discrete Geometry
• The Rectilinear Crossing Number of a Complete Graph and Sylvester's "Four Point Problem" of Geometric Probability

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