论文标题
在分层的风扇平面图纸上
On Layered Fan-Planar Graph Drawings
论文作者
论文摘要
在本文中，我们研究了使用$ h $层的风扇平面图，即适当的图纸，即边缘连接相邻层。我们表明，如果图形的嵌入是固定的，则通过将Dujmović等人的平面图的相似结果减少到$ H $中的固定参数的存在。如果嵌入未固定，则我们给出$ H = 2 $的部分结果：已经知道如何测试2个连接图的粉丝平面适当的2层图纸，并且我们在这里显示了如何为树测试它。一路上，我们为图形展示了其他有趣的结果，并具有适当的$ h $ layer图纸；特别是我们绑定了它们的路径，并表明它们具有BAR-1可见性表示。
In this paper, we study fan-planar drawings that use $h$ layers and are proper, i.e., edges connect adjacent layers. We show that if the embedding of the graph is fixed, then testing the existence of such drawings is fixed-parameter tractable in $h$, via a reduction to a similar result for planar graphs by Dujmović et al. If the embedding is not fixed, then we give partial results for $h=2$: It was already known how to test existence of fan-planar proper 2-layer drawings for 2-connected graphs, and we show here how to test this for trees. Along the way, we exhibit other interesting results for graphs with a fan-planar proper $h$-layer drawings; in particular we bound their pathwidth and show that they have a bar-1-visibility representation.
