The NonKrupp subarrangement conjecture for pseudocircle arrangements

Let A{\cal A} be a connected digon-free arrangement of pseudocircles. A triple of pseudocircles forms a triangle in A{\cal A} when its three pseudocircles bound such a triangular cell, and it is NonKrupp when it is not a Krupp configuration. Let N6Δ{\cal N}_6^\Delta denote the specified arrangement of six pseudocircles.

NonKrupp subarrangement conjecture. If every triple of pseudocircles which forms a triangle in A{\cal A} is NonKrupp, then A{\cal A} contains N6Δ{\cal N}_6^\Delta as a subarrangement.

All arrangements known to be non-circularizable by the stated theorem contain N6Δ{\cal N}_6^\Delta as a subarrangement, motivating this conjecture. Its resolution is not given in the source.

Sources & referencesView supporting material

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.