5 problems

Let $(M^3,g)$ be a closed Riemannian $3$-manifold, and let $\{\Sigma_p\}_{p\in\mathbb{N}}$ be the sequence of closed embedded minimal surfaces constructed by the min-max theory, wi…

White's conjecture. Except for finitely many values of $n$, the genus of the complete graph minus a Hamiltonian cycle equals this Euler lower bound:

Cromwell's conjecture. Then $D$ is composite.

Let $\Sigma$ be a surface and let $g(\Sigma)$ denote its genus. Fix an integer $k$ for which there is a value $\rho_0=\rho_0(g(\Sigma))$ such that every $\rho_0$-locally planar gra…

Jungerman–Ringel conjecture. Jungerman and Ringel constructed triangular embeddings of $O_{2n}$ for $n \not\equiv 2 \pmod{3}$ using orientable cascades, and conjectured that for th…