Bipartite graphs model the relationship between two disjoint sets of objects. They have a wide range of applications and are often visualized as a 2-layered drawing, where each set of objects is visualized as a set of vertices (points) on one of the two parallel horizontal lines and the relationships are represented by edges (simple curves) between the two lines connecting the corresponding vertices. One of the common objectives in such drawings is to minimize the number of crossings this, however, is computationally expensive and may still result in drawings with so many crossings that they affect the readability of the drawing. We consider a recent approach to remove crossings in such visualizations by splitting vertices, where the goal is to find the minimum number of vertices to be split to obtain a planar drawing. We show that determining whether a planar drawing exists after splitting at most $k$ vertices is fixed parameter tractable in $k$.

翻译：两组脱节天体之间的关系模式。 两组天体具有广泛的应用范围,通常可视化为两层图纸,每组天体在两条平行水平线中的一条线上可视化为一组脊椎(点),其关系由连接相应脊椎的两条线之间的边缘(简单曲线)代表。这种图纸的共同目标之一是尽量减少跨线的数量,然而,这是计算成本很高的,而且仍然可能导致图纸多处交叉,从而影响图纸的可读性。我们考虑最近的一种办法,即通过分割脊椎来去除这些可视化的交叉点,目的是找到最小的脊椎数,以获得平面图。我们表明,确定平面分后是否存在平面图,最多为$k$的顶点是固定的参数,可以美元计。