Connectivity conjecture for the triangle flip-graph of pseudocircle arrangements

About 9 years old · traced to

Let n∈Nn\in\mathbb{N}. Consider the triangle flip-graph whose vertices are all intersecting digon-free arrangements of nn pseudocircles, with edges corresponding to single triangle flips.

Triangle flip-graph connectivity conjecture. The triangle flip-graph on the set of all intersecting digon-free arrangements of nn pseudocircles is connected for every n∈Nn\in\mathbb{N}.

The analogous statement for arrangements of circles is proved in the source, while computational evidence supports the pseudocircle version for n≤7n\leq 7. The conjecture remains unresolved in the supplied text.

References

Primary source

Stefan Felsner and Manfred Scheucher, “Arrangements of Pseudocircles: On Circularizability”, arXiv:1712.02149 (2020).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.