# Structural and Complexity Aspects of Line Systems of Graphs

@inproceedings{Jirsek2010StructuralAC, title={Structural and Complexity Aspects of Line Systems of Graphs}, author={Jozef Jir{\'a}sek and Pavel Klav{\'i}k}, booktitle={ISAAC}, year={2010} }

We study line systems in metric spaces induced by graphs. A line is a subset of vertices defined by a relation of betweenness.

## 3 Citations

### A De Bruijn-Erdős Theorem in Graphs?

- Mathematics
- 2018

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 Chvatal asked whether the same statement holds true in general…

### A De Bruijn-Erd\H{o}s theorem in graphs?

- Mathematics
- 2018

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 Chv\'atal asked whether the same statement holds true in…

### Towards a de Bruijn–Erdős Theorem in the $$L_1$$-Metric

- MathematicsDiscret. Comput. Geom.
- 2013

It is proved that the answer is affirmative for sets of sets of non-collinear points in the plane with the L_1 metric, provided that no two points share their x- or y-coordinate.

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It is shown that every noncollinear set of n points in the plane determines at least n distinct lines, and a possible generalization of this theorem in the framework of metric spaces is provided.

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