3 research outputs found
The distribution of the number of small cuts in a random planar triangulation
International audienceWe enumerate rooted 3-connected (2-connected) planar triangulations with respect to the vertices and 3-cuts (2-cuts). Consequently, we show that the distribution of the number of 3-cuts in a random rooted 3-connected planar triangulation with vertices is asymptotically normal with mean and variance , and the distribution of the number of 2-cuts in a random 2-connected planar triangulation with vertices is asymptotically normal with mean and variance . We also show that the distribution of the number of 3-connected components in a random 2-connected triangulation with vertices is asymptotically normal with mean and variance  
Construction of planar triangulations with minimum degree 5
AbstractIn this article, we describe a method of constructing all simple triangulations of the sphere with minimum degree 5; equivalently, 3-connected planar cubic graphs with girth 5. We also present the results of a computer program based on this algorithm, including counts of convex polytopes of minimum degree 5