It is a longstanding conjecture that every simple drawing of a complete graph on $n \geq 3$ vertices contains a crossing-free Hamiltonian cycle. We strengthen this conjecture to "there exists a crossing-free Hamiltonian path between each pair of vertices" and show that this stronger conjecture holds for several classes of simple drawings, including strongly c-monotone drawings and cylindrical drawings. As a second main contribution, we give an overview on different classes of simple drawings and investigate inclusion relations between them up to weak isomorphism.

翻译：长期以来存在一个猜想：每个顶点数$n \geq 3$的完全图的简单绘制中都包含一个无交叉哈密顿圈。我们将此猜想强化为“每对顶点之间存在一条无交叉哈密顿路径”，并证明该强化猜想对几类简单绘制成立，包括强c-单调绘制和圆柱面绘制。作为第二个主要贡献，我们概述了不同类型的简单绘制，并研究了它们在弱同构意义下的包含关系。