**Convex-arc drawings of pseudolines**.

D. Eppstein, M. van Garderen, B. Speckmann, and T. Ueckerdt.

*21st Int. Symp. Graph Drawing*(poster), Bordeaux, France, 2013.

Springer,*Lecture Notes in Comp. Sci.*8242, 2013, pp. 522–523.

arXiv:1601.06865.

We show that every outerplanar weak pseudoline arrangement (a collection of curves topologically equivalent to lines, each crossing at most once but possibly zero times, with all crossings belonging to an infinite face) can be straightened to a hyperbolic line arrangement. As a consequence such an arrangement can also be drawn in the Euclidean plane with each pseudoline represented as a convex piecewise-linear curve with at most two bends. In contrast, for arbitrary pseudoline arrangements, a linear number of bends is sufficient and sometimes necessary.

**Geodesic paths passing through all faces on a polyhedron**.

E. Demaine, M. Demaine, D. Eppstein, H. Ito, Y. Katayama, W. Maruyama, and Y. Uno.

*24th Japan Conference on Discrete and Computational Geometry, Graphs, and Games*, 2022, pp. 58–59.

Which convex polyhedra have the property that there exist two points on the surface of the polyhedron whose shortest path passes through all of the faces of the polyhedron? The answer is yes for the tetrahedron, and for certain prisms, but no for all other regular polyhedra.

**On the biplanarity of blowups**.

D. Eppstein.

arXiv:2301.09246.

*Proc. 31st Int. Symp. Graph Drawing and Network Visualization*, Palermo, Italy, 2023 (best paper award), to appear.**Non-crossing Hamiltonian paths and cycles in output-polynomial time**.

D. Eppstein.

arXiv:2303.00147.

*Proc. 39th International Symposium on Computational Geometry (SoCG 2023)*.

Leibniz International Proceedings in Informatics (LIPIcs) 258, 2023, pp. 29:1–29:16.For any point set, the numbers of non-crossing paths, non-crossing Hamiltonian paths, non-crossing surrounding polygons, and non-crossing Hamiltonian cycles can be bounded above and below by functions of two simple parameters: the minimum number of points whose deletion leaves a collinear subset, and the number of points interior to the convex hull. Because their bounds have the same form, the numbers of the two types of paths are bounded by polynomials of each other, as are the numbers of the two types of polygons. We use these relations to list non-crossing Hamiltonian paths and polygonalizations in time polynomial in the number of outputs.

**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.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.

**The widths of strict outerconfluent graphs**.

D. Eppstein.

arXiv:2308.03967.

*Proc. 31st Int. Symp. Graph Drawing and Network Visualization*, Palermo, Italy, 2023 (poster session), to appear.

Journals – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine

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