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Graph Theory pp 149-176 | Cite as

A De Bruijn-Erdős Theorem in Graphs?

  • Vašek ChvátalEmail author
Chapter
Part of the Problem Books in Mathematics book series (PBM)

Abstract

A set of n points in the Euclidean plane determines at least n distinct lines unless these n points are collinear. In 2006, Chen and Chvátal asked whether the same statement holds true in general metric spaces, where the line determined by points x and y is defined as the set consisting of x, y, and all points z such that one of the three points x, y, z lies between the other two. The conjecture that it does hold true remains unresolved even in the special case where the metric space arises from a connected undirected graph with unit lengths assigned to edges. We trace its curriculum vitae and point out twenty-nine related open problems plus three additional conjectures.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Computer Science and Software EngineeringConcordia UniversityMontréalCanada

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