Characterizing and Recognizing 4-Map Graphs

Abstract

We characterize 4-map graphs as kite-augmented 1-planar graphs and show that they can be recognized in cubic time. For the description we use 1-planar graphs rather than maps and provide a recognition algorithm that is simpler and easier to analyze than the ones by Chen et al. (in: Proceedings of 30th annual ACM symposium on the theory of computing, STOC ’98, pp. 514–523, 1998; Algorithmica 45(2):227–262, 2006).

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Acknowledgements

I would like to thank Christian Bachmaier for many useful hints and the reviewers for their careful reading and their valuable suggestions.

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Correspondence to Franz J. Brandenburg.

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Brandenburg, F.J. Characterizing and Recognizing 4-Map Graphs. Algorithmica 81, 1818–1843 (2019). https://doi.org/10.1007/s00453-018-0510-x

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Keywords

  • Planar graphs
  • Maps
  • Map graphs
  • 1-Planar graphs
  • Graph algorithms