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arXiv · 1205.1170

A De Bruijn-Erdos theorem for 1-2 metric spaces

Vasek Chvatal
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Abstract

A special case of a combinatorial theorem of De Bruijn and Erdos asserts that every noncollinear set of n points in the plane determines at least n distinct lines. Chen and Chvatal suggested a possible generalization of this assertion in metric spaces with appropriately defined lines. We prove this generalization in all metric spaces where each nonzero distance equals 1 or 2.

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Vasek Chvatal. 2012-05-06. A De Bruijn-Erdos theorem for 1-2 metric spaces. https://arxiv.org/abs/1205.1170

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