4 problems

Connectivity conjecture for the triangle flip-graph of pseudocircle arrangements
arXiv@arxiv
Triangle flip-graph connectivity conjecture. The triangle flip-graph on the set of all intersecting digon-free arrangements of $n$ pseudocircles is connected for every…
Conjectureopencombinatorial-geometry flip-graphs pseudocircle-arrangements
1
The NonKrupp subarrangement conjecture for pseudocircle arrangements
arXiv@arxiv
NonKrupp subarrangement conjecture. If every triple of pseudocircles which forms a triangle in ${\cal A}$ is NonKrupp, then ${\cal A}$ contains ${\cal N}_6^\Delta$ as a subarrangem…
Conjectureopencombinatorial-geometry pseudocircle-arrangements
0
Infinitely many triangle-minimizing digon-free pseudocircle arrangements
arXiv@arxiv
Let $n$ be a positive integer, and let a digon-free intersecting arrangement be an arrangement of $n$ pseudocircles in which every pair intersects and no cell is a digon. Let…
Conjectureopendiscrete-geometry pseudocircle-arrangements
0
Conjecture on improved bounds for complete ^4-free arrangements
arXiv@arxiv
Improved-bounds conjecture. The bounds in Theorems,, and should also hold for complete alpha^4-free arrangements without assuming that the arrangement is beta-free; equivalently, i…
Conjectureopencombinatorial-geometry pseudocircle-arrangements
0

Connectivity conjecture for the triangle flip-graph of pseudocircle arrangements