A graph is fan-crossing free if it has a drawing in the plane so that each edge is crossed by independent edges, that is the crossing edges have distinct vertices. On the other hand, it is fan-crossing if the crossing edges have a common vertex, so that they form a fan. Both are prominent examples for beyond-planar graphs. Further well-known beyond-planar classes are the k-planar, k-gap-planar, quasi-planar, and right angle crossing graphs.

We use the subdivision, node-to-circle expansion and path-addition operations to distinguish all these graph classes. In particular, we show that the 2-subdivision and the node-to-circle expansion of any graph is fan-crossing free, which does not hold for fan-crossing and k-(gap)-planar graphs, respectively. Thereby, we obtain graphs that are fan-crossing free and neither fan-crossing nor k-(gap)-planar.

Finally, we show that some graphs have a unique fan-crossing free embedding, that there are thinned maximal fan-crossing free graphs, and that the recognition problem for fan-crossing free graphs is NP-complete.

的曲线图是风扇渡自由如果它在平面的图，使得每个边缘被独立边交叉，也就是交叉边缘具有不同的顶点。另一方面，如果交叉边缘具有相同的顶点，则是扇形交叉，从而形成扇形。两者都是平面外图的突出示例。其他众所周知的平面外类是k平面，k间隙平面，准平面和直角交叉图。

我们使用细分，节点到圆展开和路径添加操作来区分所有这些图类。特别是，我们表明任何图的2细分和节点到圆的扩展都是无扇形交叉的，这分别不适用于扇形交叉和k-（gap）-平面图。因此，我们获得了无扇形交叉且既无扇形交叉又非k-（gap）-平面的图。

最后，我们证明了某些图具有唯一的无扇形交叉自由嵌入，有变薄的最大无扇形交叉自由图，并且无扇形交叉图的识别问题是NP完全的。