Flips in two-dimensional hypertriangulations

Authors

Herbert Edelsbrunner
Alexey Garber, The University of Texas Rio Grande ValleyFollow
Mohadese Ghafari
Teresa Heiss
Morteza Saghafian

Document Type

Article

Publication Date

2-2026

Abstract

We study flips in hypertriangulations of planar points sets. Here a level-k hypertriangulation of n points in the plane is a subdivision induced by the projection of a k-hypersimplex, which is the convex hull of the barycenters of the (k−1)-dimensional faces of the standard (n−1)-simplex. In particular, we introduce four types of flips and prove that the level-2 hypertriangulations are connected by these flips.

Comments

Original published version available at https://doi.org/10.1016/j.ejc.2025.104248

Recommended Citation

Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. 2026. “Flips in Two-Dimensional Hypertriangulations.” European Journal of Combinatorics 132: 104248. https://doi.org/10.1016/j.ejc.2025.104248.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

European Journal of Combinatorics

DOI

10.1016/j.ejc.2025.104248