About and cite
The database
Jointly maintained by Austin Ulrigg and Alexander Metzger. This is a growing database of toroidal obstructions. It began with the three collections in Wendy Myrvold’s torus obstruction database. Contributions of additional graphs, references, and corrections are welcome.
Attribution and citation
Each graph record identifies its sources and discovery credit.
Reference for the initial collections
Wendy Myrvold and Jennifer Woodcock. A large set of torus obstructions and how they were discovered. The Electronic Journal of Combinatorics 25(1), P1.16 (2018).
Graph parameters
Vertex connectivity is the minimum number of vertices whose removal disconnects a connected noncomplete graph. Edge connectivity is the minimum number of edges whose removal disconnects it. Both values are zero for disconnected graphs. The vertex connectivity of a complete graph on n vertices is n − 1. Missing values are shown as “Unknown” and sort last.
Vertex and edge counts, degrees, connected components, bipartiteness, regularity, and both connectivities are computed with igraph 1.0.0. Isomorphic records are matched using Bliss canonical labeling. The graph6 data and drawings retain the first source record’s vertex labels. An exact graph6 search uses those labels.
Drawings
The surface button requests an embedding from Alexander Metzger’s genus solver. Some requests may time out or fail to produce a drawing.
Release 2026-10-12 (revision 2)
All graphs (graph6) · Parameters (CSV) · Source records and checksums