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arXiv · 1603.08974

Refining the Hierarchies of Classes of Geometric Intersection Graphs

Sergio Cabello·Miha Jejčič
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Abstract

We analyse properties of geometric intersection graphs to show the strict containment between some natural classes of geometric intersection graphs. In particular, we show the following properties: - A graph $G$ is outerplanar if and only if the 1-subdivision of $G$ is outer-segment. - For each integer $k\ge 1$, the class of intersection graphs of segments with $k$ different lengths is a strict subclass of the class of intersection graphs of segments with $k+1$ different lengths. - For each integer $k\ge 1$, the class of intersection graphs of disks with $k$ different sizes is a strict subclass of the class of intersection graphs of disks with $k+1$ different sizes. - The class of outer-segment graphs is a strict subclass of the class of outer-string graphs.

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Sergio Cabello, Miha Jejčič. 2016-03-29. Refining the Hierarchies of Classes of Geometric Intersection Graphs. https://arxiv.org/abs/1603.08974

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