Separable Drawings: Extendability and Crossing-Free Hamiltonian Cycles (opens in new tab)

Generalizing pseudospherical drawings, we introduce a new class of simple drawings, which we call separable drawings. In a separable drawing, every edge can be closed to a simple curve that intersects each other edge at most once. For different edges, the non-edge parts of these curves may interact arbitrarily though. Most notably, we show that (1) every separable drawing of any graph on $n$ vertices in the plane can be extended to a simple ...