8 problems

Ábrego et al.'s conjecture. For each positive integer $n$ multiple of $3$, there is an optimal rectilinear drawing of $K_n$ that is 3-symmetric and 3-decomposable.

3-decomposability conjecture. Every optimal set is 3-decomposable.

Asymptotic lower-bound conjecture. The rectilinear crossing number satisfies

Ábrego et al.'s conjecture. For each positive integer $n$ multiple of $3$, all crossing-minimal geometric drawings of $K_n$ have exactly

Ábrego et al.'s conjecture. For each positive integer $n$ multiple of $3$, all crossing-minimal geometric drawings of $K_n$ are $3$-decomposable.

3-symmetric optimal-drawing conjecture. For each positive integer $n$ divisible by $3$, there is an optimal geometric drawing of $K_n$ that is 3-symmetric.

3-decomposability conjecture. For each positive integer $n$ divisible by $3$, all optimal rectilinear drawings of $K_n$ are 3-decomposable.

3-decomposability and symmetry conjecture. All optimal geometric drawings are 3-decomposable, and for every positive integer $n$ divisible by $3$ there is a 3-symmetric optimal con…