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Map Graphs

Zhi-Zhong Chen·Michelangelo Grigni·Christos Papadimitriou
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Abstract

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, and a cubic time recognition algorithm for a restricted version: given a graph, decide whether it is realized by adjacencies in a map without holes, in which at most four nations meet at any point.

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Zhi-Zhong Chen, Michelangelo Grigni, Christos Papadimitriou. 1999-10-13. Map Graphs. https://arxiv.org/abs/cs/9910013

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