A classic theorem of Euclidean geometry asserts that any noncollinear set of n points in the
plane determines at least n distinct lines. Chen and Chvátal conjectured that this holds for …

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 …

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 …

A well‐known combinatorial theorem says that a set of n non‐collinear points in the plane
determines at least n distinct lines. Chen and Chvátal conjectured that this theorem extends …

A set of nn points in the plane which are not all collinear defines at least nn distinct lines.
Chen and Chvátal conjectured in 2008 that a similar result can be achieved in the broader …

The line generated by two distinct points, x and y, in a finite metric space M=(V, d), is the set
of points given by {z∈ V: d (x, y)=| d (x, z)+ d (z, y)| or d (x, y)=| d (x, z)− d (z, y)|}. It is denoted …

Number of lines in hypergraphs - ScienceDirect Skip to main contentSkip to article Elsevier
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We prove that in every metric space where no line contains all the points, there are at least
$\Omega (n^{2/3}) $ lines. This improves the previous $\Omega (\sqrt {n}) $ lower bound on …

A well-known theorem in plane geometry states that any set of n non-collinear points in the
plane determines at least n lines. Chen and Chvátal asked whether an analogous statement …

It is a classic result that a set of n non-collinear points in the Euclidean plane defines at least
n different lines. Chen and Chvátal conjectured in 2008 that the same results is true in metric …