Simple drawings are drawings of graphs in which two edges have at most one common point (either a common endpoint, or a proper crossing). It has been an open question whether every simple drawing of a complete bipartite graph $K_{m,n}$ contains a plane spanning tree as a subdrawing. We answer this question to the positive by showing that for every simple drawing of $K_{m,n}$ and for every vertex $v$ in that drawing, the drawing contains a shooting star rooted at $v$, that is, a plane spanning tree containing all edges incident to $v$.
翻译:简单的图纸是图纸的图纸,其中两个边缘最多有一个共同点(或共同端点,或适当的交叉点),这是一个未决问题,即:每张完整的双边图纸$@@@m,n}$是否每张简单的图纸就包含一个横贯树的平面图纸,作为下方图纸。我们通过显示每张简单的图纸$@m,n}$和每张顶点$v$,图纸中含有一颗以美元为单位的流星,即覆盖所有边缘事件的平面图纸,达到$v$,来回答这个问题。