Listing All Plane Graphs (Extended Abstract)
Katsuhisa Yamanaka, Shin-ichi Nakano, Tenjin-cho Kiryu · 2008
In this paper we give a simple algorithm to generate all con- nected plane graphs with at most m edges. A rooted plane graph is a plane graph with one designated (directed) edge on the outer face. The algorithm uses O(m) space and generates such graphs in O(1) time per graph on average without duplications. The algorithm does not output the entire graph but the difference from the previous graph. By modifying the algorithm we can generate all connected (non-rooted) plane graphs with at most m edges in O(m 3 ) time per graph.