Map graphs

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.

• Type: Journal
• Year: 2002
• Where: JACM
• Authors: Zhi-Zhong Chen, Michelangelo Grigni, Christos H. Papadimitriou
• Keywords: JACM 2002, Modified Notion, Planarity, Such Adjacencies