Computing in Geometry and Topology
Founding co-editor-in-chief.Locked and unlocked smooth embeddings of surfaces.
D. Eppstein.
arXiv:2206.12989.
34th Canadian Conference on Computational Geometry, 2022, pp. 135–142.
Computing in Geometry and Topology 2 (2): 5.1–5.20, 2023.If a subset of the plane has a continuous shrinking motion of itself, then every smooth isometric embedding of that subset into 3d can be smoothly flattened. However, there exist subsets of the plane with holes, for which some smooth embeddings that are topologically equivalent to a flat embedding cannot be smoothly flattened.
On the complexity of embedding in graph products.
T. Biedl, D. Eppstein, and T. Ueckerdt.
arXiv:2303.17028.
Proc. 35th Canadian Conference on Computational Geometry, 2023, pp. 77–88.
Computing in Geometry and Topology 4 (2): 5:1–5:18, 2025.Row treewidth (embedding a graph as a subgraph of a strong product of a path with a low treewidth graph), row pathwidth, and row tree-depth are all NP-hard.