Planar Map Graphs

We introduce and study a modi ed notion of planarity, in which two regions of a map are considered adjacent when they share any point of their boundaries not an edge, as standard planarity requires. We seek to characterize the graphs realized by such map adjacencies. We prove some preliminary properties of such graphs, and give a polynomial time algorithm for the following restricted problem: abstract graph, decide whether it is realized by a map in which at most four regions meet at any point. The general recognition problem remains open.

• Type: Conference
• Year: 1998
• Where: STOC
• Authors: Zhi-Zhong Chen, Michelangelo Grigni, Christos H. Papadimitriou
• Keywords: Algorithms, Modi Ed Notion, Polynomial Time Algorithm, Standard Planarity Requires, STOC 1998