Shellable drawings and the cylindrical crossing number of \(K_n\)

DOI10.1007/s00454-014-9635-0zbMath1306.05166arXiv1309.3665OpenAlexW2165284542MaRDI QIDQ2514231

Silvia Fernández-Merchant, Pedro A. Ramos, Bernardo M. Ábrego, Gelasio Salazar, Oswin Aichholzer

Publication date: 3 February 2015

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

Full work available at URL: https://arxiv.org/abs/1309.3665

zbMATH Keywords

crossing numbercomplete graphtopological drawingshellable drawingcylindrical drawing

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Graph representations (geometric and intersection representations, etc.) (05C62)

Related Items (17)

The complexity of computing the cylindrical and the \(t\)-circle crossing number of a graph ⋮ Bishellable drawings of $K_n$ ⋮ The crossing number of twisted graphs ⋮ The outerplanar crossing number of the complete bipartite graph ⋮ Bounding the tripartite‐circle crossing number of complete tripartite graphs ⋮ From art and circuit design to geometry and combinatorics ⋮ Twisted ways to find plane structures in simple drawings of complete graphs ⋮ Arc diagrams, flip distances, and Hamiltonian triangulations ⋮ Unnamed Item ⋮ On plane subgraphs of complete topological drawings ⋮ Crossing numbers and combinatorial characterization of monotone drawings of \(K_n\) ⋮ A note on the cross-index of a complete graph based on a linear tree ⋮ The bipartite-cylindrical crossing number of the complete bipartite graph ⋮ Closing in on Hill's Conjecture ⋮ Extending Drawings of Complete Graphs into Arrangements of Pseudocircles ⋮ Turán’s Brick Factory Problem: The Status of the Conjectures of Zarankiewicz and Hill ⋮ A contribution to Guy's conjecture

Uses Software

• MathOverflow

Cites Work

• Unnamed Item
• Improved enumeration of simple topological graphs
• The graph crossing number and its variants: a survey
• The 2-page crossing number of \(K_{n}\)
• Hanani–Tutte, Monotone Drawings, and Level-Planarity
• The 2-page crossing number of K _n
• Relations Between Crossing Numbers of Complete and Complete Bipartite Graphs
• On the Distribution of Crossings in Random Complete Graphs
• The crossing number of K₁₁ is 100
• On the Number of Crossings in a Complete Graph

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