MathDBThe oriented strong embedding conjecture
The oriented strong embedding conjecture
A graph is 2-connected if it is connected and has no cut vertex. A strong embedding of a graph on a surface is an embedding in which every cell is bounded by a cycle. An orientable surface is a surface with an orientation.
Oriented strong embedding conjecture. Every -connected graph has a strong embedding on some orientable surface.
This is a long-standing open problem in topological graph theory concerning the existence of strong embeddings for 2-connected graphs.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Sources & referencesView supporting material
Primary source
Meike Weiß, Reymond Akpanya and Alice C. Niemeyer, “On 3-Connected Cubic Planar Graphs and their Strong Embeddings on Orientable Surfaces”, arXiv:2509.14964 (2025).
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.