In this paper, we introduce the following new concept in graph drawing. Our task is to find a small collection of drawings such that they all together satisfy some property that is useful for graph visualization. We propose investigating a property where each edge is not crossed in at least one drawing in the collection. We call such collection uncrossed. Such property is motivated by a quintessential problem of the crossing number, where one asks for a plane drawing where the number of edge crossings is minimum. Indeed, if we are allowed to visualize only one drawing, then the one which minimizes the number of crossings is probably the neatest for the first orientation. However, a collection of drawings where each highlights a different aspect of a graph without any crossings could shed even more light on the graph's structure. We propose two definitions. First, the uncrossed number, minimizes the number of graph drawings in a collection, satisfying the uncrossed property. Second, the uncrossed crossing number, minimizes the total number of crossings in the collection that satisfy the uncrossed property. For both definitions, we establish initial results. We prove that the uncrossed crossing number is NP-hard, but there is an FPT algorithm parameterized by the solution size.

翻译：本文提出图绘制领域中的一个新概念。我们的任务是寻找一个小的绘图集合，使得这些绘图共同满足某种对图可视化有用的性质。我们研究一种性质：集合中至少有一幅绘制图使每条边不被交叉。我们将此类集合称为无交叉集合。该性质受到交叉数基本问题的启发，即寻找一个平面绘制图，使得边交叉数量最小。实际上，如果我们只能可视化一张图，那么最小化交叉数的绘制图可能是初次理解时最清晰的。然而，一个包含多幅绘图的集合，每幅图从不同角度无交叉地展示图的特性，能更深入地揭示图的结构。我们提出两个定义：第一，无交叉数，最小化满足无交叉性质的图绘制集合中的数量；第二，无交叉交叉数，最小化满足无交叉性质的集合中总交叉数。针对这两个定义，我们给出了初步结果。我们证明无交叉交叉数是NP难的，但存在一个以解大小为参数的FPT算法。