Map graphs

  title={Map graphs},
  author={Zhi-Zhong Chen and Michelangelo Grigni and Christos H. Papadimitriou},
  journal={J. ACM},
We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give an NP characterization for such graphs, derive some consequences regarding sparsity and coloring, and survey some algorithmic results. 


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