5 problems

Grünbaum's digon conjecture. Every simple arrangement of $n>2$ pairwise crossing pseudocircles has at most $2n-2$ digons.

Let ${\cal A}$ be a simple arrangement of $n\ge 3$ pairwise intersecting pseudocircles, and let $p_3({\cal A})$ denote the number of triangular cells. Triangle lower-bound conjectu…

Let ${\cal A}$ be a simple digon-free arrangement of $n$ pairwise intersecting circles, and let $p_3({\cal A})$ denote the number of triangular cells. Weak Grünbaum triangle conjec…

Strengthened pseudocircle-arrangement conjectures. The following three statements hold:

Infinite-family conjecture. There exists an infinite family of simple arrangement graphs of 4-edge-critical arrangements of pseudocircles.