The non-planarity of \(K_{5}\) and \(K_{3,3}\) as axioms for plane ordered geometry

DOI10.1007/s00022-012-0129-zzbMath1267.51012OpenAlexW2021161503MaRDI QIDQ1926115

Victor V. Pambuccian

Publication date: 27 December 2012

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-012-0129-z

zbMATH Keywords

non-planar graphPasch axiomsplitting an axiomordered planeouter form of the Pasch axiom

Mathematics Subject Classification ID

Axiomatic and generalized convexity (52A01) Foundations of classical theories (including reverse mathematics) (03B30) Ordered geometries (ordered incidence structures, etc.) (51G05)

Related Items (2)

On the simplicity of ordered geometry ⋮ Aristotle's problem

Cites Work

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• The axiomatics of ordered geometry: I. Ordered incidence spaces
• Another splitting of the Pasch axiom
• Weakly ordered plane geometry
• Planar graphs and poset dimension
• A proof of Pasch's axiom in the absolute theory of oriented parallelity
• Bemerkungen zum Vierfarbenproblem
• Forms of the Pasch axiom in ordered geometry
• The Erdos-Szekeres problem on points in convex position – a survey
• Convex Maps

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