# Recognizing embedded caterpillars with weak unit disk contact representations is NP-hard

@article{Chiu2020RecognizingEC, title={Recognizing embedded caterpillars with weak unit disk contact representations is NP-hard}, author={Man-Kwun Chiu and Jonas Cleve and Martin N{\"o}llenburg}, journal={ArXiv}, year={2020}, volume={abs/2010.01881} }

Weak unit disk contact graphs are graphs that admit a representation of the nodes as a collection of internally disjoint unit disks whose boundaries touch if there is an edge between the corresponding nodes. We provide a gadget-based reduction to show that recognizing embedded caterpillars that admit a weak unit disk contact representation is NP-hard.

## 3 Citations

### Weak Unit Disk Contact Representations for Graphs without Embedding

- Mathematics, Computer ScienceArXiv
- 2020

This work gives a linear time algorithm to recognize whether a caterpillar, a graph where every node is adjacent to or on a central path, allows a weak unit disk contact representation, and shows that it is NP-hard to decide whether a tree allows such a representation.

### Recognition of Unit Disk Graphs for Caterpillars, Embedded Trees, and Outerplanar Graphs

- Computer Science, MathematicsArXiv
- 2021

This work shows that the recognition of unit disk graphs remains NP-hard for outerplanar graphs and for embedded trees, and shows that given a caterpillar graph, one can decide in linear time whether it is a unit disk graph.

### Unit Disk Representations of Embedded Trees, Outerplanar and Multi-legged Graphs

- Mathematics, Computer ScienceGD
- 2021

This work proves that it is NP-hard to decide if an outerplanar graph or an embedded tree admits a unit disk contact representation (UDC), and provides a linear-time decidable characterization of caterpillar graphs that admit a UDR.

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