Planar graph algorithms constitute a pivotal area in theoretical computer science, addressing problems where graphs can be drawn on a plane without edge crossings. Among the myriad challenges in this ...

We regard a graph $G$ as a set $\{1,\ldots,v\}$ together with a nonempty set $E$ of two-element subsets of $\{1,\ldots,v\}$. Let $p = (p_1,\ldots,p_v)$ be an element ...

Origami (paper folding) is an effective tool for transforming two-dimensional materials into three-dimensional structures, and has been widely applied to robots, deployable structures, metamaterials, ...