6 problems

Let $L_n$ be the perimeter of the convex hull of the multiple random walks, and let ${\mathcal G}_n$ and ${\mathcal E}^{\mathrm{f}}_n$ be the sets defined in the paper. For each re…

Let $n\ge3$ be odd, and let $G$ be a complete geometric graph on $n$ vertices that can be decomposed into $\left\lceil\frac{n}{2}\right\rceil+1$ plane star-forests. Convex-hull-siz…

Agoston et al.'s conjecture. A convex hull thrackle on $n$ points has at most $n$ convex hulls.

Locally valid-cut conjecture. The intersection of $\mathcal{R}_{\mathrm{shor}} \cap \mathcal{R}_{\mathrm{ksoc}}$ with the locally valid cuts captures $\mathcal{G}$.

Tightness conjecture. The intersection

Polynomial stabilization conjecture. The iterative construction stabilizes after a polynomially bounded number of iterations: