Extending Drawings of Complete Graphs into Arrangements of Pseudocircles

DOI10.1137/20M1313234zbMath1465.05117arXiv2001.06053MaRDI QIDQ4992833

Alan Arroyo, Matthew Sunohara, R. Bruce Richter

Publication date: 10 June 2021

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.06053

zbMATH Keywords

drawings of complete graphspseudolinear drawingspseudospherical drawings

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Erd?s problems and related topics of discrete geometry (52C10) Graph representations (geometric and intersection representations, etc.) (05C62) Planar arrangements of lines and pseudolines (aspects of discrete geometry) (52C30)

Related Items (4)

Convex drawings of the complete graph: topology meets geometry ⋮ Topological drawings meet classical theorems from convex geometry ⋮ Unnamed Item ⋮ Topological Drawings Meet Classical Theorems from Convex Geometry

Uses Software

• MathOverflow

Cites Work

• Unnamed Item
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• New lower bounds for the number of \((\leq k)\)-edges and the rectilinear crossing number of \(K_{n}\)
• The 2-page crossing number of \(K_{n}\)
• Shellable drawings and the cylindrical crossing number of \(K_n\)
• A lower bound for the rectilinear crossing number
• Bishellable drawings of $K_n$
• Drawings of Kn with the same rotation scheme are the same up to Reidemeister moves. Gioan's Theorem
• Levi's Lemma, pseudolinear drawings of , and empty triangles
• On the Distribution of Crossings in Random Complete Graphs
• The unavoidable arrangements of pseudocircles
• On the Number of Crossings in a Complete Graph
• Extending Drawings of Graphs to Arrangements of Pseudolines
• Arrangements of pseudocircles: on circularizability
• Arrangements of pseudocircles: on circularizability

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