Sylvester-Gallai theorem and metric betweenness

DOI10.1007/s00454-003-0795-6zbMath1053.51006OpenAlexW1540677203MaRDI QIDQ1880209

Vašek Chvátal

Publication date: 22 September 2004

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

Full work available at URL: https://doi.org/10.1007/s00454-003-0795-6

zbMATH Keywords

Sylvester-Gallai theoremmetric betweenness

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Axiomatic and generalized convexity (52A01) Metric geometry (51F99) Ordered geometries (ordered incidence structures, etc.) (51G05) Other finite incidence structures (geometric aspects) (51E30)

Related Items (18)

Lines, betweenness and metric spaces ⋮ Lines in bipartite graphs and in 2‐metric spaces ⋮ On subbetweennesses of trees: hardness, algorithms, and characterizations ⋮ Strict betweennesses induced by posets as well as by graphs ⋮ A constructive version of the Sylvester-Gallai theorem ⋮ A New Class of Graphs That Satisfies the Chen‐Chvátal Conjecture ⋮ Towards a de Bruijn-Erdős theorem in the \(L_1\)-metric ⋮ Finite Sholander trees, trees, and their betweenness ⋮ Lines in hypergraphs ⋮ Topologies induced by the representation of a betweenness relation as a family of order relations ⋮ Problems related to a de Bruijn-Erdös theorem ⋮ De Bruijn-Erdős-type theorems for graphs and posets ⋮ The axiomatics of ordered geometry: I. Ordered incidence spaces ⋮ Betweenness structures of small linear co-size ⋮ Pretrees and the shadow topology ⋮ A de Bruijn-Erdős theorem for chordal graphs ⋮ Graph metric with no proper inclusion between lines ⋮ Some betweenness relation topologies induced by simplicial complexes

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