3 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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The 3-decomposable optimality conjecture for $(\leq k)$ -edges and crossing numbers
3-decomposable optimality conjecture. For every $k$ and $n$ , the class of $3$ -decomposable sets contains optimal sets for both $E_{\leq k}(n)$ and $\overline{\operatorname{cr}}(n)$ …
Conjectureopengeometric-combinatorics halving-edges rectilinear-crossingsarXiv posted 2 days ago
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The unrestricted-point-set conjectures for $(\leq k)$ -edges and crossing numbers
Let $P$ be an unrestricted point-set of $n$ points in the plane. Write $E_{\leq k}(P)$ for the number of edges of the geometric complete graph on $P$ incident to at most $k$ points…
Conjectureopengeometric-combinatorics halving-edges rectilinear-crossingsarXiv posted 2 days ago

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