论文标题
$ k_n $的广义扭曲图中的空三角形
Empty Triangles in Generalized Twisted Drawings of $K_n$
论文作者
论文摘要
简单的图纸是平面或球体上的图形图，使顶点是不同的点，边缘是连接其端点的Jordan弧，并且边缘最多一次相交（在适当的交叉处或共享端点中）。如果有一个点$ o $，则简单的图纸是概括性的，以便每件散发出$ o $的射线最多一次，最多一次，并且有一条从$ o $散发出的射线，该射线完全跨越了每个边缘。我们表明，$ k_n $的所有广义扭曲图纸都完全包含$ 2N-4 $空的三角形，这是迈向证明$ k_n $的每一个简单图纸就是这种情况的重要一步。
Simple drawings are drawings of graphs in the plane or on the sphere such that vertices are distinct points, edges are Jordan arcs connecting their endpoints, and edges intersect at most once (either in a proper crossing or in a shared endpoint). Simple drawings are generalized twisted if there is a point $O$ such that every ray emanating from $O$ crosses every edge of the drawing at most once and there is a ray emanating from $O$ which crosses every edge exactly once. We show that all generalized twisted drawings of $K_n$ contain exactly $2n-4$ empty triangles, by this making a substantial step towards proving the conjecture that this is the case for every simple drawing of $K_n$.
