Summary: Generating Rooted Triangulations with Minimum Degree Four
David Avis Chiu Ming Kong
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 \Lambda
n such that any other triangulation En 6=
n in the set can be transformed to E \Lambda
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 nonisomorphic 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.
1.1 Maximal Planar Graphs and Diagonal Transformation
A simple planar graph is maximal planar if and only if it is triangulated. Hence a triangulation