Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777338 | European Journal of Combinatorics | 2018 | 16 Pages |
Abstract
We study flip-graphs of triangulations on topological surfaces where distance is measured by counting the number of necessary flip operations between two triangulations. We focus on surfaces of positive genus g with a single boundary curve and n marked points on this curve and consider triangulations up to homeomorphism with the marked points as their vertices. Our results are bounds on the maximal distance between two triangulations. Our lower bounds assert that these distances grow at least like 5nâ2 for all gâ¥1. Our upper bounds grow at most like [4â1â(4g)]n for gâ¥2, and at most like 23nâ8 for the bordered torus.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Hugo Parlier, Lionel Pournin,