Connectivity conjecture for the triangle flip-graph of pseudocircle arrangements

From papers

Let nNn\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 nNn\in\mathbb{N}.

The analogous statement for arrangements of circles is proved in the source, while computational evidence supports the pseudocircle version for n7n\leq 7. The conjecture remains unresolved in the supplied text.

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Sources & referencesView supporting material

Primary source

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

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