# Simultaneous Embeddability of Two Partitions

@article{Athenstdt2014SimultaneousEO, title={Simultaneous Embeddability of Two Partitions}, author={Jan Christoph Athenst{\"a}dt and Tanja Hartmann and Martin N{\"o}llenburg}, journal={ArXiv}, year={2014}, volume={abs/1408.6019} }

We study the simultaneous embeddability of a pair of partitions of the same underlying set into disjoint blocks. Each element of the set is mapped to a point in the plane and each block of either of the two partitions is mapped to a region that contains exactly those points that belong to the elements in the block and that is bounded by a simple closed curve. We establish three main classes of simultaneous embeddability weak, strong, and full embeddability that differ by increasingly strict…

## 3 Citations

### C-Planarity Testing of Embedded Clustered Graphs with Bounded Dual Carving-Width

- Mathematics, Computer ScienceIPEC
- 2019

It is shown that the C-Planarity Testing problem admits a single-exponential single-parameter FPT (resp, XP) algorithm for embedded flat (resp., non-flat) clustered graphs, when parameterized by the carving-width of the dual graph of the input.

### Planarity of Overlapping Clusterings Including Unions of Two Partitions

- Computer ScienceJ. Graph Algorithms Appl.
- 2017

We show that clustered planarity with overlapping clusters as introduced by Didimo et al. can be solved in polynomial time if each cluster induces a connected subgraph. It can be solved in linear…

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