2 problems

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Optimality conjecture for the lower bound on $(\leq k)$ -edges
Optimality conjecture. Based on computational experiments, the bound is optimal for
Conjectureopendiscrete-geometry k-edges rectilinear-crossingsarXiv posted 2 days ago
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Ábrego et al.'s minimum $(\leq k)$ -edge conjecture for crossing-minimal drawings
Ábrego et al.'s conjecture. For each positive integer $n$ multiple of $3$ , all crossing-minimal geometric drawings of $K_n$ have exactly
Conjectureopencombinatorial-geometry k-edges rectilinear-crossing-numberarXiv posted 2 days ago

Optimality conjecture for the lower bound on (≤k)(\leq k)(≤k)-edges