A De Bruijn–Erdős theorem for chordal graphs
Abstract
A special case of a combinatorial theorem of De Bruijn and Erd˝ os asserts that every noncollinear set of n points in the plane determines at least n distinct lines. Chen and Chvátal suggested a possible generalization of this assertion in metric spaces with appropriately defined lines. We prove this generalization in all metric spaces induced by connected chordal graphs.
Domains
Mathematics [math]
Origin : Publication funded by an institution
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