Characterizing and Recognizing 4-Map Graphs

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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