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A De Bruijn-Erdos theorem for chordal graphs (1201.6376v1)
Published 30 Jan 2012 in math.CO
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 induced by connected chordal graphs.
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