Abstract
A "based" plane triangulation is a plane triangulation with one designated edge on the outer face. In this paper we give a simple algorithm to generate all 4-connected based plane triangulations with at most n vertices. This is the first algorithm to generate such triangulations. The algorithm uses O(n) space and generates such triangulations in O(n) time per triangulation without duplications. By modifying the algorithm one can generate all 4-connected (non-based) plane triangulations with at most n vertices in O(n^2) time per triangulation without duplications.
