6 problems

Let $A$ be a point set in general position in the plane, let $A_I$ be its set of interior points, and for each $W\subseteq A_I$ let $\mathcal{PT}_{W}(A)$ denote the pseudo-triangul…

Refinement conjecture. If $(G,\rho)$ is refined to $(G',\rho)$ without adding vertices, then $(G',\rho)$ is good too.

Let $n$ denote the size parameter of the input plane graph, and consider the embedding algorithms developed in the paper for producing pseudo-triangulation embeddings. The near-lin…

Let $G$ be a plane graph. A plane graph is generically rigid if its generic realizations are infinitesimally rigid, and it can be straightened as a pseudo-triangulation if its embe…

Let $S$ be a point set, let $W\subset S$ be a subset of its interior points, and let $v\in W$. Write ${\mathsf{pt}_{W}}(S)$ for the number of pseudo-triangulations of $S$ in which…

Let $S$ be a finite point set. Write ${\mathsf{ppt}}(S)$ for the number of pointed pseudo-triangulations of $S$ and ${\mathsf{tr}}(S)$ for the number of triangulations of $S$. The…