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Algorithmica

, Volume 81, Issue 5, pp 1818–1843 | Cite as

Characterizing and Recognizing 4-Map Graphs

  • Franz J. BrandenburgEmail author
Article

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).

Keywords

Planar graphs Maps Map graphs 1-Planar graphs Graph algorithms 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.PassauGermany

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