次三次图的平面Lombardi图
Planar Lombardi Drawings for Subcubic Graphs
摘要：
我们证明了每个最大度为3的平面图都有一个平面图，其中边被画成围绕每个顶点以相等角度相交的圆弧。我们的建设是基于Koebe-Thurston-Andreev圆包装定理，并使用一种新的类型的沃罗诺伊图的圆包装，是不变的Moebius变换，使用三维双曲几何定义。我们还使用圆包装，以建设平面Lombardi图纸的一类特殊的4-正则平面图，中间图的多面体图，我们表明，并不是每一个4-正则平面图有一个Lombardi图纸。我们已经实现了我们的算法3连通平面三次图。
英文摘要：
We prove that every planar graph with maximum degree three has a planar drawing in which the edges are drawn as circular arcs that meet at equal angles around every vertex. Our construction is based on the Koebe-Thurston-Andreev circle packing theorem, and uses a novel type of Voronoi diagram for circle packings that is invariant under Moebius transformations, defined using three-dimensional hyperbolic geometry. We also use circle packing to construct planar Lombardi drawings of a special class of 4-regular planar graphs, the medial graphs of polyhedral graphs, and we show that not every 4-regular planar graph has a Lombardi drawing. We have implemented our algorithm for 3-connected planar cubic graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
