 
Summary: GENERATING ROOTED TRIANGULATIONS WITHOUT
REPETITIONS
David Avis*
School of Computer Science
McGill University
3480 University
Montr’eal, Qu’ebec, Canada
H3A 2A7
ABSTRACT
We use the reverse search technique to give algorithms for generating all
graphs on n points that are two and three connected planar triangulations with r
points on the outer face. The triangulations are rooted, which means the outer
face has a fixed labelling. The triangulations are produced without duplications
in O(n 2 ) time per triangulation. The algorithms use O(n) space. A program for
generating all 3connected rooted triangulations based on this algorithm is avail
able by ftp.
1. Introduction
Let G = (V , E) be a planar graph with vertex set V = {v 1 , . . . , v n }, and let 3 £ r £ n be an
integer. G is an r  rooted triangulation if it can be embedded in the plane such that the outer
face has labels {v 1 , . . . , v r } in clockwise order, and all interior faces are triangles. A vertex ( or
