Connectivity conjecture for the triangle flip-graph of pseudocircle arrangements
Let . Consider the triangle flip-graph whose vertices are all intersecting digon-free arrangements of 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 pseudocircles is connected for every .
The analogous statement for arrangements of circles is proved in the source, while computational evidence supports the pseudocircle version for . 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).
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