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… 

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