8 problems

Conjecture on diagonal-flip stabilization. The only surfaces $S$ for which

Conjecture on nonseparating cycle types. If $g \geq 3$ is odd, every triangulation of $N_g$ has a nonseparating cycle that is one-sided and orientable-leaving, one that is one-side…

Nonorientable analogue of Thomassen's conjecture. Every such triangulation contains an NSC such that the two surfaces separated by the NSC have Euler genera $h$ and $g-h$, respecti…

Characteristic-zero exterior shifting conjecture.

Lex-segment prevalence conjecture. As $n$ tends to infinity,

Lexicographic edge conjecture. If $\sigma<_{\mathrm{lex}}\sigma'$, then

Let $G$ be a graph with a triangulation $T$ of a surface $S$ as a spanning subgraph. A graph is globally rigid when its generic realization is uniquely determined, up to Euclidean…

Let $(\Sigma,\mathbb{M})$ be a positive-genus surface with empty boundary and exactly two punctures, and let $\tau$ be a tagged triangulation of $(\Sigma,\mathbb{M})$. Write…