On \(\leq k\)-edges, crossings, and halving lines of geometric drawings of \(K _{n }\)

DOI10.1007/s00454-012-9403-yzbMath1247.52010OpenAlexW1670552514MaRDI QIDQ443913

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

Publication date: 13 August 2012

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-012-9403-y

zbMATH Keywords

\(k\)-sets\(k\)-edgesallowable sequencesgeometric drawingshalving linesrectilinear crossing numbers

Mathematics Subject Classification ID

Erd?s problems and related topics of discrete geometry (52C10)

Related Items (17)

On the rectilinear crossing number of complete uniform hypergraphs ⋮ The rectilinear local crossing number of \(K_{n}\) ⋮ A lower bound on the crossing number of uniform hypergraphs ⋮ Bishellable drawings of $K_n$ ⋮ The 2-page crossing number of \(K_{n}\) ⋮ Rectilinear crossings in complete balanced \(d\)-partite \(d\)-uniform hypergraphs ⋮ From art and circuit design to geometry and combinatorics ⋮ Maximum rectilinear crossing number of uniform hypergraphs ⋮ Approximating the Rectilinear Crossing Number ⋮ The 3-symmetric pseudolinear crossing number of \(K_{36}\) ⋮ Crossing numbers and combinatorial characterization of monotone drawings of \(K_n\) ⋮ New algorithms and bounds for halving pseudolines ⋮ Reconstruction of the crossing type of a point set from the compatible exchange graph of noncrossing spanning trees ⋮ An improvement of the lower bound on the maximum number of halving lines in planar sets with 32 points ⋮ Reconstruction of the Crossing Type of a Point Set from the Compatible Exchange Graph of Noncrossing Spanning Trees ⋮ NOTE ON THE NUMBER OF OBTUSE ANGLES IN POINT SETS ⋮ Approximating the rectilinear crossing number

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Improving the crossing lemma by finding more crossings in sparse graphs
• Geometric drawings of \(K_{n}\) with few crossings
• An extended lower bound on the number of(\(\leqslant k\))-edges to generalized configurations of points and the pseudolinear crossing number of \(K_n\)
• 3-symmetric and 3-decomposable geometric drawings of \(K_n\)
• More on k-sets of finite sets in the plane
• On the combinatorial classification of nondegenerate configurations in the plane
• Improved bounds for planar \(k\)-sets and related problems
• A characterization of planar graphs by pseudo-line arrangements
• On halving line arrangements
• Point sets that minimize \((\leq k)\)-edges, 3-decomposable drawings, and the rectilinear crossing number of \(K_{30}\)
• 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
• New results on lower bounds for the number of (⩽ k)-facets
• 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
• Abstract order type extension and new results on the rectilinear crossing number
• Crossing Number Problems
• Point sets with many \(k\)-sets

This page was built for publication: On \(\leq k\)-edges, crossings, and halving lines of geometric drawings of \(K _{n }\)