Generating Rooted Triangulations with Minimum Degree Four
David Avis, Chiu Ming Kong · Canadian Conference on Computational Geometry · 1996
A graph is a triangulation if it is planar and every face is a triangle. A triangulation is rooted if the external triangular face is labelled. Two rooted triangulations with the same external face labels are isomorphic if their internal vertices can be labelled so that both triangulations have identical edge lists. In this article, we show that in the set of rooted triangulations on n points with minimum degree four, there exists a target triangulation E n such that any other triangulation En 6= E n in the set can be transformed to E n via a finite sequence of single and double diagonal transformations. Using this result with the reverse search technique, we present an algorithm for generating all non-isomorphic rooted triangulations on n points with minimum degree four. The triangulations are produced without repetitions in O(n 2 ) time per triangulation. The algorithm uses O(n) space. 1 Background 1.1 Maximal Planar Graphs and Diagonal Transformation A simple planar gr...