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

Václav Chvátal (2014)

Czechoslovak Mathematical Journal

A special case of a combinatorial theorem of De Bruijn and Erdős 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 where each nonzero distance equals 1 or 2 .

Disjoint and complete unions of incidence structures

František Machala, Marek Pomp (1997)

Mathematica Bohemica

Some decompositions of general incidence structures with regard to distinguished components (modular or simple) are considered and several structure theorems for them are deduced.

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