On the size of chromatic Delaunay mosaics
R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, Discrete and Computational Geometry 75 (2026) 24–47.

On the MST-ratio: Theoretical bounds and complexity of finding the maximum
A. Jabal Ameli, F. Motiei, M. Saghafian, in:, 20th International Conference and Workshops on Algorithms and Computation, Springer Nature, 2026, pp. 386–401.

Order-2 Delaunay triangulations optimize angles
H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).

Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality
M. Mahini, H. Beigy, S. Qadami, M. Saghafian, Information Sciences 719 (2025).

Tight bounds between the Jensen–Shannon divergence and the minmax divergence
A. Akopyan, H. Edelsbrunner, Z. Virk, H. Wagner, Entropy 27 (2025).

Discrete microlocal Morse theory
A. Brown, O. Draganov, Journal of Pure and Applied Algebra 229 (2025).

Flips in two-dimensional hypertriangulations
H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, European Journal of Combinatorics 132 (2025).

Chromatic alpha complexes
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, Foundations of Data Science 8 (2025) 30–62.

Maximum Betti numbers of cech complexes
H. Edelsbrunner, J. Pach, Discrete &; Computational Geometry (2025).

Identifying cobordisms using kernel persistence
Y. Bleile, L. Fajstrup, T. Heiss, A.M. Svane, S.S. Sørensen, ArXiv (n.d.).

Average and expected distortion of Voronoi paths and scapes
H. Edelsbrunner, A. Nikitenko, Discrete &; Computational Geometry 73 (2025) 490–499.

Burning or collapsing the medial axis is unstable
E.W. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, La Matematica 4 (2025) 811–828.

Methods for fluid simulation, surface tracking, and statistics of non-manifold structures
P. Synak, Methods for Fluid Simulation, Surface Tracking, and Statistics of Non-Manifold Structures, Institute of Science and Technology Austria, 2025.

On angles in higher order Brillouin tessellations and related tilings in the plane
H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.

The ultimate frontier: An optimality construction for homotopy inference (media exposition)
D. Attali, H. Kourimska, C.D. Fillmore, I. Ghosh, A. Lieutier, E.R. Stephenson, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.

The Euclidean MST-ratio for bi-colored lattices
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, in:, 32nd International Symposium on Graph Drawing and Network Visualization, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.

Depth in arrangements: Dehn–Sommerville–Euler relations with applications
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578.

The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms
H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.

Maximum Betti numbers of cech complexes
H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.

Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds
D. Attali, H. Kourimska, C.D. Fillmore, I. Ghosh, A. Lieutier, E.R. Stephenson, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, p. 11:1-11:19.